Einstein metrics on homogeneous superspacesThis paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a…Yang Zhang, Mark D. Gould, Artem Pulemotov et al.·Nov 21, 2024SaveLearn
Effective actions, cutoff regularization, quasi-locality, and gluing of partition functionsThe paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of…A. V. Ivanov·Nov 21, 2024SaveLearn
Time-harmonic waves in Korteweg and nematic-Korteweg fluidsWe derive the Helmholtz--Korteweg equation, which models acoustic waves in Korteweg fluids. We further derive a nematic variant of the Helmholtz-Korteweg equation, which incorporates an additional…Patrick E. Farrell, Umberto Zerbinati·Nov 20, 2024SaveLearn
Trace formula for quantum chaotic systems with geometrical symmetries and spinWe derive a Gutzwiller-type trace formula for quantum chaotic systems that accounts for both particle spin precession and discrete geometrical symmetries. This formula generalises previous results…Vaios Blatzios, Christopher H. Joyner, Sebastian Müller et al.·Nov 19, 2024SaveLearn
Magnetic tunneling between disc-shaped obstaclesIn this paper we derive formulae for the semiclassical tunneling in the presence of a constant magnetic field in 2 dimensions. The `wells' in the problem are identical discs with Neumann boundary…Søren Fournais, Léo Morin·Nov 19, 2024SaveLearn
Poisson structure of the 4-vertex model, and the higher-spin XXX chain, and Yang-Baxter algebrasWe implement the quantum inverse scattering method for the 4-vertex model. In comparison to previous works of the author which examined the 6-vertex, and 20-vertex, models, the 4-vertex model…Pete Rigas·Nov 19, 2024SaveLearn
Asymptotic behavior for a finitely degenerate semilinear pseudo-parabolic equationThis paper investigates the initial boundary value problem of a finitely degenerate semilinear pseudo-parabolic equation associated with H\"ormander's operator. Based on the global existence of…Xiang-kun Shao, Xue-song Li, Nan-jing Huang et al.·Nov 19, 2024SaveLearn
Exact physical quantities of the XYZ spin chain in the thermodynamic limitThe thermodynamic limits of the XYZ spin chain with periodic or twisted boundary conditions are studied. By using the technique of characterizing the eigenvalue of the transfer matrix by the T-Q…Zhirong Xin, Junpeng Cao, Wen-Li Yang et al.·Nov 19, 2024SaveLearn
Evolving the Euler rotation axis as a dynamical system, using the Euler vector and generalizationsDifferential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is also known as a…John H. Elton, John R. Elton·Nov 18, 2024SaveLearn
Topological Dynamics of Synthetic MoleculesWe study the dynamics of synthetic molecules whose architectures are generated by space transformations from a point group acting on seed resonators. We show that the dynamical matrix of any such…Yuming Zhu, Emil Prodan·Nov 18, 2024SaveLearn
Existence of Boutroux curves, g-functions and spectral networks from Newton's polygonWe prove the existence of an algebraic plane curve of equation P(x,y)=0, with prescribed asymptotic behaviors at punctures, and with the Boutroux property, namely, periods have vanishing real part,…Bertrand Eynard, Soufiane Oukassi·Nov 18, 2024SaveLearn
Scaling of the Lyapunov exponent at a balanced hyperbolic critical pointIn both the random hopping model and at topological phase transitions in one-dimensional chiral systems, the Lyapunov exponent vanishes at zero energy, but is here shown to have an inverse…Joris De Moor, Christian Sadel, Hermann Schulz-Baldes·Nov 17, 2024SaveLearn
On one-parameter families of hermiticity-preserving superoperators which are not positiveA one-parameter family of hermiticity-preserving superoperators is a time-dependent family \tn(C)→Mn(C)\t∈R of…Grzegorz Pastuszak, Alicja Jaworska-Pastuszak, Takeo Kamizawa et al.·Nov 17, 2024SaveLearn
On the degeneracy of the energy levels of Schroedinger and Klein-Gordon equations on Riemannian coveringsWe study the degeneracy of the energy levels of the Schroedinger equation with Kepler-Coulomb potential and of the Klein-Gordon equation on Riemannian coverings of the Euclidean space and of the…Claudia Maria Chanu, Giovanni Rastelli·Nov 16, 2024SaveLearn
Asymptotic expansion of the partition function for β-ensembles with complex potentialsIn this work we establish under certain hypotheses the N +∞ asymptotic expansion of integrals of the form ZN,[V] \, = \, ∫N Π a < bN(za -…Alice Guionnet, Karol Kozlowski, Alex Little·Nov 15, 2024SaveLearn
Radiant Field Theory: A Transport Approach to Shaped Wave Transmission through Disordered MediaWe present a field-theoretic framework to characterize the distribution of transmission eigenvalues for coherent wave propagation through disordered media. The central outcome is a transport equation…David Gaspard, Arthur Goetschy·Nov 15, 2024SaveLearn
Transmission eigenvalue distribution in disordered media from radiant field theoryWe develop a field-theoretic framework, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a…David Gaspard, Arthur Goetschy·Nov 15, 2024SaveLearn
On fluctuations of Coulomb systems and universality of the Heine distributionWe consider a class of external potentials on the complex plane C for which the coincidence set to the obstacle problem contains a Jordan curve in the exterior of the droplet. We refer to…Yacin Ameur, Joakim Cronvall·Nov 15, 2024SaveLearn
Wigner function under changes of reference framesIn this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral…J. Berra-Montiel, G. F. Torres del Castillo·Nov 15, 2024SaveLearn
Petz-R\'enyi relative entropy in QFT from modular theoryWe consider the generalization of the Araki-Uhlmann formula for relative entropy to Petz-R\'enyi relative entropy. We compute this entropy for a free scalar field in the Minkowski wedge between the…Markus B. Fröb, Leonardo Sangaletti·Nov 14, 2024SaveLearn
Discrete Dirac structures and discrete Lagrange--Dirac dynamical systems in mechanicsIn this paper, we propose the concept of ()-discrete Dirac structures over a manifold, where we define ()-discrete two-forms on the manifold and incorporate discrete constraints using…Linyu Peng, Hiroaki Yoshimura·Nov 14, 2024SaveLearn
Euler's original derivation of elastica equationEuler derived the differential equations of elastica by the variational method in 1744, but his original derivation has never been properly interpreted or explained in terms of modern mathematics. We…Shigeki Matsutani·Nov 14, 2024SaveLearn
Simons Lectures on Categorical SymmetriesGlobal Categorical Symmetries are a powerful new tool for analyzing quantum field theories. This volume compiles lecture notes from the 2022 and 2023 summer schools on Global Categorical Symmetries,…Davi Costa, Clay Córdova, Michele Del Zotto et al.·Nov 13, 2024SaveLearn
Circulant graphs as an example of discrete quantum unique ergodicityA discrete analog of quantum unique ergodicity was proved for Cayley graphs of quasirandom groups by Magee, Thomas and Zhao. They show that for large graphs there exist real orthonormal basis of…Jon Harrison, Clare Pruss·Nov 13, 2024SaveLearn
The Non-Commutative Brillouin Torus, a Non-Commutative Geometry perspectiveNon-commutative geometry has significantly contributed to quantum mechanics by providing mathematical tools to extract topological and geometrical information from these systems. This thesis explores…Juan Florez·Nov 13, 2024SaveLearn