Spectral Analysis of Non-unitary Two-phase Quantum Walks in One DimensionIt is recently shown by Asahara-Funakawa-Seki-Tanaka that existing index theory for chirally symmetric (discrete-time) quantum walks can be extended to the setting of non-unitary quantum walks. More…Chusei Kiumi, Kei Saito, Yohei Tanaka·May 23, 2022SaveLearn
Another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivityIn the preceding papers, imposing certain complicated and strong conditions, the present author showed that the solution to the BCS-Bogoliubov gap equation in superconductivity is twice…Shuji Watanabe·May 23, 2022SaveLearn
New conserved integrals and invariants of radial compressible flow in n>1 dimensionsConserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in n>1 dimensions. Apart from entropy, which is a well-know invariant,…Stephen C. Anco, Sara Seifi, Amanullah Dar·May 22, 2022SaveLearn
On an elastic strain-limiting special Cosserat rod modelMotivated by recent strain-limiting models for solids and biological fibers, we introduce the first intrinsic set of nonlinear constitutive relations, between the geometrically exact strains and the…K. R. Rajagopal, Casey Rodriguez·May 22, 2022SaveLearn
Exact surface energy of the D(1)2 spin chain with generic non-diagonal boundary reflectionsThe exact solution of the D(1)2 quantum spin chain with generic non-diagonal boundary reflections is obtained. It is found that the generating functional of conserved quantities of the system…Guang-Liang Li, Yi Qiao, Junpeng Cao et al.·May 22, 2022SaveLearn
Gauge Symmetry in Shape DynamicsC. N. Yang's ideas about local gauge symmetry and non-integrable phases have been enormously fertile sources of inspiration in fundamental physics and in the quantum theory of matter. They also…Frank Wilczek·May 22, 2022SaveLearn
An Ising-type formulation of the six-vertex modelWe show that the celebrated six-vertex model of statistical mechanics (along with its multistate generalizations) can be reformulated as an Ising-type model with only a two-spin interaction. Such a…Vladimir V. Bazhanov, Sergey M. Sergeev·May 22, 2022SaveLearn
Quantum Covariance and FilteringWe give a tutorial exposition of the analogue of the filtering equation for quantum systems focusing on the quantum probabilistic framework and developing the ideas from the classical theory. Quantum…John E. Gough·May 22, 2022SaveLearn
A continuum framework for phase field with bulk-surface dynamicsThis continuum mechanical theory aims at detailing the underlying rational mechanics of dynamic boundary conditions proposed by Fischer, Maass, & Dieterich [1], Goldstein, Miranville, & Schimperna…Luis Espath·May 21, 2022SaveLearn
Integrable boundaries for the q-Hahn processTaking inspiration from the harmonic process with reservoirs introduced by Giardinà, Kurchan and the author in arXiv:1904.01048, we propose integrable boundary conditions for its trigonometric…Rouven Frassek·May 21, 2022SaveLearn
Noether symmetries and first integrals of damped harmonic oscillatorNoether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped…M. Umar Farooq, M. Safdar·May 21, 2022SaveLearn
Weak anisotropic Hardy inequality: essential self-adjointness of drift-diffusion operators on domains in Rd, revisitedWe consider the problem of essential self-adjointness of the drift-diffusion operator H=-1ρ∇· ρ D∇ +V on domains Ω⊂ Rd with C2-boundary…Gheorghe Nenciu, Irina Nenciu·May 21, 2022SaveLearn
Generalised graph Laplacians and canonical Feynman integrals with kinematicsTo any graph with external half-edges and internal masses, we associate canonical integrals which depend non-trivially on particle masses and momenta, and are always finite. They are generalised…Francis Brown·May 20, 2022SaveLearn
A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous mediumWe derive a new eight dimensional matrix representation of the Maxwell equations for a linear homogeneous medium and extend it to the case of a linear inhomogneous medium. This derivation starts ab…Sameen Ahmed Khan, Ramaswamy Jagannathan·May 20, 2022SaveLearn
From Lieb-Robinson Bounds to Automorphic EquivalenceI review the role of Lieb-Robinson bounds in characterizing and utilizing the locality properties of the Heisenberg dynamics of quantum lattice systems. In particular, I discuss two definitions of…Bruno Nachtergaele·May 20, 2022SaveLearn
Onset of pattern formation in thin ferromagnetic films with perpendicular anisotropyWe consider the onset of pattern formation in an ultrathin ferromagnetic film of the form Ωt := Ω × [0,t] for Ω R2 with preferred perpendicular…Birger Brietzke, Hans Knüpfer·May 20, 2022SaveLearn
2D Toda τ Functions, Weighted Hurwitz Numbers and the Cayley Graph: Determinant Representation and Recursion FormulaWe generalize the determinant representation of the KP τ functions to the case of the 2D Toda τ functions. The generating functions for the weighted Hurwitz numbers are a parametric family of 2D…Xiang-Mao Ding, Xiang Li·May 20, 2022SaveLearn
The theory of screws derived from a module over the dual numbersThe theory of screws clarifies many analogies between apparently unrelated notions in mechanics, including the duality between forces and angular velocities. It is known that the real 6-dimensional…E. Minguzzi·May 19, 2022SaveLearn
Time-dependent contact mechanicsContact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact…Manuel de León, Jordi Gaset, Xavier Gràcia et al.·May 19, 2022SaveLearn
Generalized Nijenhuis Torsions and block-diagonalization of operator fieldsThe theory of generalized Nijenhuis torsions, which extends the classical notions due to Nijenhuis and Haantjes, offers new tools for the study of normal forms of operator fields. We propose a…Daniel Reyes Nozaleda, Piergiulio Tempesta, Giorgio Tondo·May 19, 2022SaveLearn
Local operators in the Sine-Gordon model: ∂μ φ \, ∂ φ and the stress tensorWe consider the simplest non-trivial local composite operators in the massless Sine-Gordon model, which are ∂μ φ \, ∂ φ and the stress tensor Tμ. We show that…Markus B. Fröb, Daniela Cadamuro·May 18, 2022SaveLearn
Topological phases of unitary dynamics: Classification in Clifford categoryA quantum cellular automaton (QCA) or a causal unitary is by definition an automorphism of local operator algebra, by which local operators are mapped to local operators. Quantum circuits of small…Jeongwan Haah·May 18, 2022SaveLearn
Category of Quantizations and Inverse ProblemWe introduce a category composed of all quantizations of all Poisson algebras. By the category, we can treat in a unified way the various quantizations for all Poisson algebras and develop a new…Akifumi Sako·May 18, 2022SaveLearn
Universal characteristics of deep neural network loss surfaces from random matrix theoryThis paper considers several aspects of random matrix universality in deep neural networks. Motivated by recent experimental work, we use universal properties of random matrices related to local…Nicholas P Baskerville, Jonathan P Keating, Francesco Mezzadri et al.·May 17, 2022SaveLearn
Wedge domains in non-compactly causal symmetric spacesThis article is part of an ongoing project aiming at the connections between causal structures on homogeneous spaces, Algebraic Quantum Field Theory (AQFT), modular theory of operator algebras and…Karl-Hermann Neeb, Gestur Olafsson·May 16, 2022SaveLearn