tag:blogger.com,1999:blog-87249712352702307992018-03-06T14:00:40.640-08:00Mathematical PhysicsSite for <a href="http://communitypeerreview.blogspot.com/">Community Peer Review</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.comBlogger7676125tag:blogger.com,1999:blog-8724971235270230799.post-44977478344723832962013-08-06T00:00:00.039-07:002013-08-06T00:00:34.207-07:001308.0708 (Jacob Chapman et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0708">Localization for random block operators related to the XY spin chain</a> [<a href="http://arxiv.org/pdf/1308.0708">PDF</a>]</h2>Jacob Chapman, Günter Stolz<a name='more'></a><blockquote class="abstract">We study a class of random block operators which appear as effective one-particle Hamiltonians for the anisotropic XY quantum spin chain in an exterior magnetic field given by an array of i.i.d. random variables. For arbitrary non-trivial single-site distribution of the magnetic field, we prove dynamical localization of these operators at non-zero energy.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0708">http://arxiv.org/abs/1308.0708</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-7743644325746210462013-08-06T00:00:00.037-07:002013-08-06T00:00:33.360-07:001308.0737 (T. Andreussi et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0737">Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically<br /> Accessible Stability - Theory</a> [<a href="http://arxiv.org/pdf/1308.0737">PDF</a>]</h2>T. Andreussi, P. J. Morrison, F. Pegoraro<a name='more'></a><blockquote class="abstract">Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e. variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0737">http://arxiv.org/abs/1308.0737</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-48709475128380904452013-08-06T00:00:00.035-07:002013-08-06T00:00:32.336-07:001308.0755 (Jian Xu et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0755">Leading-order temporal asymptotics of the Fokas-Lenells Equation without<br /> solitons</a> [<a href="http://arxiv.org/pdf/1308.0755">PDF</a>]</h2>Jian Xu, Engui Fan<a name='more'></a><blockquote class="abstract">We use the Deift-Zhou method to obtain, in the solitonless sector, the leading order asymptotic of the solution to the Cauchy problem of the Fokas-Lenells equation as $t\ra+\infty$ on the full-line.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0755">http://arxiv.org/abs/1308.0755</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-64298415638756100422013-08-06T00:00:00.033-07:002013-08-06T00:00:31.244-07:001308.0815 (F. Caruso et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0815">Solving a two-electron quantum dot model in terms of polynomial<br /> solutions of a Biconfluent Heun Equation</a> [<a href="http://arxiv.org/pdf/1308.0815">PDF</a>]</h2>F. Caruso, J. Martins, V. Oguri<a name='more'></a><blockquote class="abstract">The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigeinfunctions for the Schr\"odinger equation describing the relative motion of the electrons.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0815">http://arxiv.org/abs/1308.0815</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-62117991372552964032013-08-06T00:00:00.031-07:002013-08-06T00:00:30.266-07:001308.0858 (Mayer Humi)<h2 class="title"><a href="http://arxiv.org/abs/1308.0858">Convective Equations and a Generalized Cole-Hopf Transformation</a> [<a href="http://arxiv.org/pdf/1308.0858">PDF</a>]</h2>Mayer Humi<a name='more'></a><blockquote class="abstract">Differential equations with convective terms such as the Burger's equation appear in many applications and have been the subject of intense research. In this paper we use a generalized form of Cole-Hopf transformation to relate the solutions of some of these nonlinear equations to the solutions of linear equations. In particular we consider generalized forms of Burger's equation and second order nonlinear ordinary differential equations with convective terms which can represent steady state one-dimensional convection.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0858">http://arxiv.org/abs/1308.0858</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-60045306865954376792013-08-06T00:00:00.029-07:002013-08-06T00:00:29.309-07:001308.0874 (J. P. Montillet)<h2 class="title"><a href="http://arxiv.org/abs/1308.0874">The Generalization of the Decomposition of Functions by Energy operators<br /> (Part II) and some Applications</a> [<a href="http://arxiv.org/pdf/1308.0874">PDF</a>]</h2>J. P. Montillet<a name='more'></a><blockquote class="abstract">This work introduces the families of generalized energy operators $([[.]^p]_k^+)_{k\in\mathbb{Z}}$ and $([[.]^p]_k^-)_{k\in\mathbb{Z}}$ ($p$ in $\mathbb{Z}^+$). One shows that with $\bold{Lemma}$ 1, the successive derivatives of $\big ([[$f$]^{p-1}]_1^+ \big)^n$ ($n$ in $\mathbb{Z}$, $n\neq 0$) can be decomposed with the generalized energy operators $\big ([[.]^p]_k^+\big)_{k\in\mathbb{Z}}$ when $f$ is in the subspace $\mathbf{S}_p^-(\mathbb{R})$. With $\bold{Theorem}$ 1 and $f$ in $\mathbf{s}_p^-(\mathbb{R})$, one can decompose uniquely the successive derivatives of $\big ([[$f$]^{p-1}]_1^+ \big)^n$ ($n$ in $\mathbb{Z}$, $n\neq 0$) with the generalized energy operators $\big ([[.]^p]_k^+\big)_{k\in\mathbb{Z}}$ and $\big ([[.]^p]_k^-\big)_{k\in\mathbb{Z}}$. $\mathbf{S}_p^-(\mathbb{R})$ and $\mathbf{s}_p^-(\mathbb{R})$ ($p$ in $\mathbb{Z}^+$) are subspaces of the Schwartz space $\mathbf{S}^-(\mathbb{R})$. These results generalize the work of [arxiv/1208.3385]. The second fold of this work is the application of the generalized energy operator families onto the solutions of linear partial differential equations. As an example, the theory is applied to the Helmholtz equation. Note that in this specific case, the use of generalized energy operators in the general solution of this PDE extends the results of [montilletIMF45-48-2010]. Finally, this work ends with some numerical examples. In particular, when defining the Poynting vector and intensity with generalized energy operators applied onto the planar electromagnetic waves, this allows to define a linear relationship with the radiation pressure force.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0874">http://arxiv.org/abs/1308.0874</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-90196445344070623812013-08-06T00:00:00.027-07:002013-08-06T00:00:28.279-07:001308.0911 (Volker Bach et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0911">Continuous Renormalization Group Analysis of Spectral Problems in<br /> Quantum Field Theory</a> [<a href="http://arxiv.org/pdf/1308.0911">PDF</a>]</h2>Volker Bach, Miguel Ballesteros, Jürg Fröhlich<a name='more'></a><blockquote class="abstract">The isospectral renormalization group is a powerful method to analyze the spectrum of operators in quantum field theory. It was introduced in 1995 [see \cite{BachFrohlichSigal1995}, \cite{BachFrohlichSigal1998}] and since then it has been used to prove several results for non-relativistic quantum electrodynamics. After the introduction of the method there have been many works in which extensions, simplifications or clarifications are presented (see \cite{BachChenFrohlichSigal2003}, \cite{GriesemerHasler2008}, \cite{FrohlichGriesemerSigal2009}). In this paper we present a new approach in which we construct a flow of operators parametrized by a continuous variable in the positive real axis. While this is in contrast to the discrete iteration used before, this is more in spirit of the original formulation of the renormalization group introduced in theoretical physics in 1974 \cite{KogutWilson1974}. The renormalization flow that we construct can be expressed in a simple way: it can be viewed as a single application of the Feshbach-Schur map with a clever selection of the spectral parameter. Another advantage of the method is that there exists a flow function for which the renormalization group that we present is the orbit under this flow of an initial Hamiltonian. This opens the possibility to study the problem using different techniques coming from the theory of evolution equations.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0911">http://arxiv.org/abs/1308.0911</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-80667999316024213082013-08-06T00:00:00.025-07:002013-08-06T00:00:27.342-07:001308.0920 (Michael Leitner et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0920">Nonlinear differential identities for cnoidal waves</a> [<a href="http://arxiv.org/pdf/1308.0920">PDF</a>]</h2>Michael Leitner, Alice Mikikits-Leitner<a name='more'></a><blockquote class="abstract">This article presents a family of nonlinear differential identities for the spatially periodic function $u_s(x)$, which is essentially the Jacobian elliptic function $\cn^2(z;m(s))$ with one non-trivial parameter $s$. More precisely, we show that this function $u_s$ fulfills equations of the form {equation*} \big(u_s^{(\alpha)}u_s^{(\beta)}\big)(x)=\sum_{n=0}^{2+\alpha+\beta}b_{\alpha,\beta}(n)u_s^{(n)}(x)+c_{\alpha,\beta}, {equation*} for any $s>0$ and for all $\alpha,\beta\in\N_0$. We give explicit expressions for the coefficients $b_{\alpha,\beta}(n)$ and $c_{\alpha,\beta}$ for given $s$. Moreover, we show that for any $s$ satisfying $\sinh(\pi/(2s))\geq 1$ the set of functions $\{1,u^{\vphantom{a}}_s,u'_s,u"_s,...\}$ constitutes a basis for $L^2(0,2\pi)$. By virtue of our formulas the problem of finding a periodic solution to any nonlinear wave equation reduces to a problem in the coefficients. A finite ansatz exactly solves the KdV equation (giving the well-known cnoidal wave solution) and the Kawahara equation. An infinite ansatz is expected to be especially efficient if the equation to be solved can be considered a perturbation of the KdV equation.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0920">http://arxiv.org/abs/1308.0920</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-81885862026061092092013-08-06T00:00:00.023-07:002013-08-06T00:00:26.259-07:001308.0982 (Sudhaker Upadhyay)<h2 class="title"><a href="http://arxiv.org/abs/1308.0982">Finite field dependent BRST transformations and its applications to<br /> gauge field theories</a> [<a href="http://arxiv.org/pdf/1308.0982">PDF</a>]</h2>Sudhaker Upadhyay<a name='more'></a><blockquote class="abstract">The Becchi-Rouet-Stora and Tyutin (BRST) transformation plays a crucial role in the quantization of gauge theories. The BRST transformation is also very important tool in characterizing the various renormalizable field theoretic models. The generalization of the usual BRST transformation, by making the infinitesimal global parameter finite and field dependent, is commonly known as the finite field dependent BRST (FFBRST) transformation. In this thesis, we have extended the FFBRST transformation in an auxiliary field formulation and have developed both on-shell and off-shell FF-anti-BRST transformations. The different aspects of such transformation are studied in Batalin-Vilkovisky (BV) formulation. FFBRST transformation has further been used to study the celebrated Gribov problem and to analyze the constrained dynamics in gauge theories. A new finite field dependent symmetry (combination of FFBRST and FF-anti-BRST) transformation has been invented. The FFBRST transformation is shown useful in connection of first-class constrained theory to that of second-class also. Further, we have applied the Batalin-Fradkin-Vilkovisky (BFV) technique to quantize a field theoretic model in the Hamiltonian framework. The Hodge de Rham theorem for differential geometry has also been studied in such context.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0982">http://arxiv.org/abs/1308.0982</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-32094054657911861732013-08-06T00:00:00.021-07:002013-08-06T00:00:25.190-07:001308.0998 (Miguel Angel Alejo et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0998">Dynamics of complex-valued modified KdV solitons with applications to<br /> the stability of breathers</a> [<a href="http://arxiv.org/pdf/1308.0998">PDF</a>]</h2>Miguel Angel Alejo, Claudio Muñoz<a name='more'></a><blockquote class="abstract">We study the long-time dynamics of complex-valued modified Korteweg-de Vries (mKdV) solitons, which are recognized because they blow-up in finite time. We establish stability properties at the H^1 level of regularity, uniformly away from each blow-up point. These new properties are used to prove that mKdV breathers are H^1 stable, improving our previous result, where we only proved H^2 stability. The main new ingredient of the proof is the use of a B\"acklund transformation which links the behavior of breathers, complex-valued solitons and small real-valued solutions of the mKdV equation. We also prove that negative energy breathers are asymptotically stable. Since we do not use any method relying on the Inverse Scattering Transformation, our proof works even under rough perturbations, provided a corresponding local well-posedness theory is available.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0998">http://arxiv.org/abs/1308.0998</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-51888173718139436492013-08-06T00:00:00.019-07:002013-08-06T00:00:24.348-07:001308.1003 (Arno B. J. Kuijlaars et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.1003">Singular values of products of Ginibre random matrices, multiple<br /> orthogonal polynomials and hard edge scaling limits</a> [<a href="http://arxiv.org/pdf/1308.1003">PDF</a>]</h2>Arno B. J. Kuijlaars, Lun Zhang<a name='more'></a><blockquote class="abstract">Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation kernel that can be expressed in terms of Meijer G-functions. We show that this point process can be interpreted as a multiple orthogonal polynomial ensemble. We give integral representations for the relevant multiple orthogonal polynomials and a new double contour integral for the correlation kernel, which allows us to find its scaling limits at the origin (hard edge). The limiting kernels generalize the classical Bessel kernels. For M=2 they coincide with the scaling limits found by Bertola, Gekhtman, and Szmigielski in the Cauchy-Laguerre two-matrix model, which indicates that these kernels represent a new universality class in random matrix theory.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1003">http://arxiv.org/abs/1308.1003</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-26947455851285549772013-08-06T00:00:00.017-07:002013-08-06T00:00:19.622-07:001308.1005 (Batu Güneysu et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.1005">The profinite dimensional manifold structure of formal solution spaces<br /> of formally integrable PDE's</a> [<a href="http://arxiv.org/pdf/1308.1005">PDF</a>]</h2>Batu Güneysu, Markus J. Pflaum<a name='more'></a><blockquote class="abstract">In this paper, we study the formal solution space of a nonlinear PDE in a fiber bundle. To this end, we start with foundational material and introduce the notion of a pfd structure to build up a new concept of profinite dimensional manifolds. We show that the infinite jet space of the fiber bundle is a profinite dimensional manifold in a natural way. The formal solution space of the nonlinear PDE then is a subspace of this jet space, and inherits from it the structure of a profinite dimensional manifold, if the PDE is formally integrable. We apply our concept to scalar PDE's and prove a new criterion for formal integrability of such PDE's. In particular, this result entails that the Euler-Lagrange Equation of a relativistic scalar field with a polynomial self-interaction is formally integrable.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1005">http://arxiv.org/abs/1308.1005</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-32124675741692901922013-08-06T00:00:00.015-07:002013-08-06T00:00:17.567-07:001308.1046 (Jean-Philippe Michel et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.1046">Second order symmetries of the conformal Laplacian</a> [<a href="http://arxiv.org/pdf/1308.1046">PDF</a>]</h2>Jean-Philippe Michel, Fabian Radoux, Josef Šilhan<a name='more'></a><blockquote class="abstract">Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by differential operators of second order. They are constructed from conformal Killing 2-tensors satisfying a natural and conformally invariant condition. As a consequence, we get also the classification of the second order symmetries of the conformal Laplacian. Our results generalize the ones of Eastwood and Carter, which hold on conformally flat and Einstein manifolds respectively. We illustrate our results on two examples and apply them to the R-separation of variables of the conformally invariant Laplace equation.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1046">http://arxiv.org/abs/1308.1046</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-40015494034379042672013-08-06T00:00:00.013-07:002013-08-06T00:00:16.630-07:001308.1052 (Steven Duplij)<h2 class="title"><a href="http://arxiv.org/abs/1308.1052">Formulation of singular theories in a partial Hamiltonian formalism<br /> using a new bracket and multi-time dynamics</a> [<a href="http://arxiv.org/pdf/1308.1052">PDF</a>]</h2>Steven Duplij<a name='more'></a><blockquote class="abstract">A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller than the number of velocities) is proposed. The equations of motion become first-order differential equations, and they coincide with those of multi-time dynamics, if a certain condition is imposed. In a singular theory, this condition is fulfilled in the case of the coincidence of the number of generalized momenta with the rank of the Hessian matrix. The noncanonical generalized velocities satisfy a system of linear algebraic equations, which allows an appropriate classification of singular theories (gauge and nongauge). A new antisymmetric bracket (similar to the Poisson bracket) is introduced, which describes the time evolution of physical quantities in a singular theory. The origin of constraints is shown to be a consequence of the (unneeded in our formulation) extension of the phase space. In this case the new bracket transforms into the Dirac bracket. Quantization is briefly discussed.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1052">http://arxiv.org/abs/1308.1052</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-83493494689821783772013-08-06T00:00:00.011-07:002013-08-06T00:00:15.677-07:001308.1057 (Sean O'Rourke et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.1057">Universality of local eigenvalue statistics in random matrices with<br /> external source</a> [<a href="http://arxiv.org/pdf/1308.1057">PDF</a>]</h2>Sean O'Rourke, Van Vu<a name='more'></a><blockquote class="abstract">Consider a random matrix of the form W_n = M_n + D_n, where M_n is a Wigner matrix and D_n is a real deterministic diagonal matrix (D_n is commonly referred to as an external source in the mathematical physics literature). We study the universality of the local eigenvalue statistics of W_n for a general class of Wigner matrices M_n and diagonal matrices D_n. Unlike the setting of many recent results concerning universality, the global semicircle law fails for this model. However, we can still obtain the universal sine kernel formula for the correlation functions. This demonstrates the remarkable phenomenon that local laws are more resilient than global ones. The universality of the correlation functions follows from a four moment theorem, which we prove using a variant of the approach used earlier by Tao and Vu.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1057">http://arxiv.org/abs/1308.1057</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-643912911624827622013-08-06T00:00:00.009-07:002013-08-06T00:00:14.481-07:001308.1061 (Yoann Dabrowski et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.1061">Functional properties of Hörmander's space of distributions having a<br /> specified wavefront set</a> [<a href="http://arxiv.org/pdf/1308.1061">PDF</a>]</h2>Yoann Dabrowski, Christian Brouder<a name='more'></a><blockquote class="abstract">The space $D'_\Gamma$ of distributions having their wavefront sets in a closed cone $\Gamma$ has become important in physics because of its role in the formulation of quantum field theory in curved space time. In this paper, the topological and bornological properties of $D'_\Gamma$ and its dual $E'_\Lambda$ are investigated. It is found that $D'_\Gamma$ is a nuclear, semi-reflexive and semi-Montel complete normal space of distributions. Its strong dual $E'_\Lambda$ is a nuclear, barrelled and bornological normal space of distributions which, however, is not even sequentially complete. Concrete rules are given to determine whether a distribution belongs to $D'_\Gamma$, whether a sequence converges in $D'_\Gamma$ and whether a set of distributions is bounded in $D'_\Gamma$.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1061">http://arxiv.org/abs/1308.1061</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-25130209256598915842013-08-06T00:00:00.007-07:002013-08-06T00:00:13.175-07:001308.1063 (J. LaChapelle)<h2 class="title"><a href="http://arxiv.org/abs/1308.1063">Functional Mellin Transforms</a> [<a href="http://arxiv.org/pdf/1308.1063">PDF</a>]</h2>J. LaChapelle<a name='more'></a><blockquote class="abstract">Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows a construction of functional Mellin transforms. In turn, the functional Mellin transforms can be used to define functional traces, logarithms, and determinants. The associated functional integrals are useful tools for probing function spaces in general and $C^\ast$-algebras in particular. Several interesting aspects are explored. As an application, we construct a functional Mellin representation of the quantum evolution operator.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1063">http://arxiv.org/abs/1308.1063</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-78514460684298079122013-08-06T00:00:00.005-07:002013-08-06T00:00:12.289-07:001308.1064 (Stan Alama et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.1064">Stability of symmetric vortices for two-component Ginzburg-Landau<br /> systems</a> [<a href="http://arxiv.org/pdf/1308.1064">PDF</a>]</h2>Stan Alama, Qi Gao<a name='more'></a><blockquote class="abstract">We study Ginzburg-Landau equations for a complex vector order parameter. We consider the Dirichlet problem in the disk in the plane with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation of the energy. We find that the stability of the degree-one equivariant solution depends on both the Ginzburg-Landau parameter as well as the sign of the interaction term in the energy.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1064">http://arxiv.org/abs/1308.1064</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-10689705854567507802013-08-06T00:00:00.003-07:002013-08-06T00:00:11.363-07:001308.1065 (Sören Petrat et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.1065">Multi-Time Schrödinger Equations Cannot Contain Interaction Potentials</a> [<a href="http://arxiv.org/pdf/1308.1065">PDF</a>]</h2>Sören Petrat, Roderich Tumulka<a name='more'></a><blockquote class="abstract">Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,...,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics, and sometimes arise also in quantum field theory. The evolution of a wave function with $N$ time variables is governed by $N$ Schr\"odinger equations, one for each time variable. These Schr\"odinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the $N$ Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schr\"odinger equations that the presence of interaction potentials leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles. We also prove a result that seemingly points in the opposite direction: When a cut-off length $\delta>0$ is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schr\"odinger equations with interaction potentials of range $\delta$ are consistent; however, in the desired limit $\delta\to 0$ of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1065">http://arxiv.org/abs/1308.1065</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-67192577691857216322013-08-06T00:00:00.001-07:002013-08-06T00:00:07.779-07:001308.1076 (Alcides Garat)<h2 class="title"><a href="http://arxiv.org/abs/1308.1076">The equivalence between local inertial frames and electromagnetic gauge<br /> in Einstein-Maxwell theories</a> [<a href="http://arxiv.org/pdf/1308.1076">PDF</a>]</h2>Alcides Garat<a name='more'></a><blockquote class="abstract">We are going to prove that locally the inertial frames and gauge states of the electromagnetic field are equivalent. This proof will be valid for Einstein-Maxwell theories in four-dimensional Lorentzian spacetimes. Use will be made of theorems proved in a previous manuscript. These theorems state that locally the group of electromagnetic gauge transformations is isomorphic to the local Lorentz transformations of a special set of tetrad vectors. The tetrad that locally and covariantly diagonalizes any non-null electromagnetic stress-energy tensor. Two isomorphisms, one for each plane defined locally by two separate sets of two vectors each. In particular, we are going to use the plane defined by the timelike and one spacelike vector, plane or blade one. These results will be extended to any tetrad that results in a local Lorentz transformation of the special tetrad that locally and covariantly diagonalizes the stress-energy tensor.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1076">http://arxiv.org/abs/1308.1076</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-65918595831835278822013-08-05T00:00:00.013-07:002013-08-05T00:00:18.160-07:001105.5303 (Stephen C. Anco et al.)<h2 class="title"><a href="http://arxiv.org/abs/1105.5303">Exact Solutions of Nonlinear Partial Differential Equations by the<br /> Method of Group Foliation Reduction</a> [<a href="http://arxiv.org/pdf/1105.5303">PDF</a>]</h2>Stephen C. Anco, Sajid Ali, Thomas Wolf<a name='more'></a><blockquote class="abstract">A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this group-foliation reduction method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation.</blockquote>View original: <a href="http://arxiv.org/abs/1105.5303">http://arxiv.org/abs/1105.5303</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-8062862431740356632013-08-05T00:00:00.011-07:002013-08-05T00:00:16.904-07:001112.0817 (Martin Maria Kovár)<h2 class="title"><a href="http://arxiv.org/abs/1112.0817">A New Causal Topology and Why the Universe is Co-compact</a> [<a href="http://arxiv.org/pdf/1112.0817">PDF</a>]</h2>Martin Maria Kovár<a name='more'></a><blockquote class="abstract">We show that there exists a canonical topology, naturally connected with the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by quantum gravity. Taking a causal site compatible with Minkowski space, on every compact subset our topology became a reconstruction of the original topology of the spacetime (only from its causal structure). From the global point of view, the reconstructed topology is the de Groot dual or co-compact with respect to the original, Euclidean topology. The result indicates that the causality is the primary structure of the spacetime, carrying also its topological information.</blockquote>View original: <a href="http://arxiv.org/abs/1112.0817">http://arxiv.org/abs/1112.0817</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-49274024217683436422013-08-05T00:00:00.009-07:002013-08-05T00:00:14.931-07:001308.0467 (V. M. Simulik et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0467">Structure and different realizations of the extended real Clifford-Dirac<br /> algebra</a> [<a href="http://arxiv.org/pdf/1308.0467">PDF</a>]</h2>V. M. Simulik, I. Yu. Krivsky, I. O. Gordievich, I. L. Lamer<a name='more'></a><blockquote class="abstract">The structure of the 64-dimensional extended real Clifford-Dirac (ERCD) algebra, which has been introduced in our paper Phys. Lett. A. 375 (2011) 2479, is under consideration. The subalgebras of this algebra are investigated: the 29-dimensional proper ERCD algebra and 32-dimensional pure matrix algebra of invariance of the Dirac equation in the Foldy-Wouthuysen representation. The last one is the maximal pure matrix algebra of invariance of this equation. The different realizations of the proper ERCD algebra are given. The application of proper ERCD algebra is illustrated on the example of the derivation of the hidden spin (1,0) Poincare symmetry of the Dirac equation.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0467">http://arxiv.org/abs/1308.0467</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-4732184915330959102013-08-05T00:00:00.007-07:002013-08-05T00:00:13.860-07:001308.0500 (Valery B. Morozov)<h2 class="title"><a href="http://arxiv.org/abs/1308.0500">Method of problem solution of diffraction and scattering theory</a> [<a href="http://arxiv.org/pdf/1308.0500">PDF</a>]</h2>Valery B. Morozov<a name='more'></a><blockquote class="abstract">Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier. Method potentiality is discussed.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0500">http://arxiv.org/abs/1308.0500</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-8724971235270230799.post-75227443973261995682013-08-05T00:00:00.005-07:002013-08-05T00:00:09.330-07:001308.0504 (Enrico De Micheli et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0504">Inverse optical imaging viewed as a backward channel communication<br /> problem</a> [<a href="http://arxiv.org/pdf/1308.0504">PDF</a>]</h2>Enrico De Micheli, Giovanni Alberto Viano<a name='more'></a><blockquote class="abstract">The inverse problem in optics, which is closely related to the classical question of the resolving power, is reconsidered as a communication channel problem. The main result is the evaluation of the maximum number $M_\epsilon$ of $\epsilon$-distinguishable messages ($\epsilon$ being a bound on the noise of the image) which can be conveyed back from the image to reconstruct the object. We study the case of coherent illumination. By using the concept of Kolmogorov's $\epsilon$-capacity, we obtain: $M_\epsilon ~ 2^{S \log(1/\epsilon)} \to \infty$ as $\epsilon \to 0$, where S is the Shannon number. Moreover, we show that the $\epsilon$-capacity in inverse optical imaging is nearly equal to the amount of information on the object which is contained in the image. We thus compare the results obtained through the classical information theory, which is based on the probability theory, with those derived from a form of topological information theory, based on Kolmogorov's $\epsilon$-entropy and $\epsilon$-capacity, which are concepts related to the evaluation of the massiveness of compact sets.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0504">http://arxiv.org/abs/1308.0504</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0