Causal and self-dual morphisms in four complex dimensionsWe define a class of maps between holomorphically embedded null curves which generalize conformal transformations, and can be defined in any complex dimension. In four dimensions, we can also define…Edward B. Baker·Mar 15, 2022SaveLearn
Discrete approximations to Dirac operators and norm resolvent convergenceWe consider continuous Dirac operators defined on Rd, d∈\1,2,3\, together with various discrete versions of them. Both forward-backward and symmetric finite differences are used as…Horia D. Cornean, Henrik Garde, Arne Jensen·Mar 15, 2022SaveLearn
Return probability of quantum and correlated random walksThe analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and…Chusei Kiumi, Norio Konno, Shunya Tamura·Mar 15, 2022SaveLearn
Optimal mixing for two-state anti-ferromagnetic spin systemsWe prove an optimal Ω(n-1) lower bound for modified log-Sobolev (MLS) constant of the Glauber dynamics for anti-ferromagnetic two-spin systems with n vertices in the tree uniqueness regime.…Xiaoyu Chen, Weiming Feng, Yitong Yin et al.·Mar 15, 2022SaveLearn
A short note on the appearance of the simplest antilinear ODE in several physical contextsIn this short note, we review several one-dimensional problems such as those involving linear Schroedinger equation, variable-coefficient Helmholtz equation, Zakharov-Shabat system and Kubelka-Munk…Dmitry Ponomarev·Mar 14, 2022SaveLearn
Hamiltonians for polaron models with subcritical ultraviolet singularitiesWe treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity,…Jonas Lampart·Mar 14, 2022SaveLearn
New simple Lie superalgebras as queerified associative algebrasOver C, Montgomery superized Herstein's construction of simple Lie algebras from finite-dimensional associative algebras, found obstructions to the procedure and applied it to…Dimitry Leites·Mar 14, 2022SaveLearn
A hyperbolic Kac-Moody Calogero modelA new kind of quantum Calogero model is proposed, based on a hyperbolic Kac-Moody algebra. We formulate nonrelativistic quantum mechanics on the Minkowskian root space of the simplest rank-3…Olaf Lechtenfeld, Don Zagier·Mar 12, 2022SaveLearn
Integrable bi-Hamiltonian systems by Jacobi structure on real three-dimensional Lie groupsBy Poissonization of Jacobi structures on real three-dimensional Lie groups G and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on…H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam·Mar 12, 2022SaveLearn
Dynamical symmetry algebra of two superintegrable two-dimensional systemsA complete classification of 2D superintegrable systems on two-dimensional conformally flat spaces has been performed over the years and 58 models, divided into 12 equivalence classes, have been…Ian Marquette, Christiane Quesne·Mar 12, 2022SaveLearn
Causal perturbative QED and white noise. The inductive stepWe present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically…Jaroslaw Wawrzycki·Mar 11, 2022SaveLearn
Causal perturbative QED and white noiseWe present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically…Jaroslaw Wawrzycki·Mar 11, 2022SaveLearn
Bogoliubov's causal perturbative QED and white noise. Interacting fieldsWe present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically…Jaroslaw Wawrzycki·Mar 11, 2022SaveLearn
Bogoliubov's causal perturbative QFT with Hida operatorsWe will present the axioms of Bogoliubov's causal perturbative QFT in which the creation-annihilation operators are interpreted as Hida operators. We will shortly present the results that can be…Jaroslaw Wawrzycki·Mar 11, 2022SaveLearn
A trace inequality of Ando, Hiai and Okubo and a monotonicity property of the Golden-Thompson inequalityThe Golden-Thompson trace inequality which states that Tr\, eH+K ≤ Tr\, eH eK has proved to be very useful in quantum statistical mechanics. Golden used it to show that the classical free…Eric A. Carlen, Elliott H. Lieb·Mar 11, 2022SaveLearn
The state of the Lieb--Thirring conjectureIn 1976 Lieb and Thirring established upper bounds on sums of powers of the negative eigenvalues of a Schrödinger operator in terms of semiclassical phase-space integrals. Over the last 45 years the…Lukas Schimmer·Mar 11, 2022SaveLearn
Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetryWe show that non-trivial two-dimensional topological insulators protected by an odd time-reversal symmetry have absolutely continuous edge spectrum. The proof employs a time-reversal symmetric…Alex Bols, Christopher Cedzich·Mar 10, 2022SaveLearn
On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomialsThis work reports and classifies the most general construction of rational quantum potentials in terms of the generalized Hermite polynomials. This is achieved by exploiting the intrinsic relation…Ian Marquette, Kevin Zelaya·Mar 10, 2022SaveLearn
A family of orthogonal polynomials corresponding to Jacobi matrices with a trace class inverseAssume that \an;\,n≥0\ is a sequence of positive numbers and Σ an\,-1<∞. Let αn=kan, βn=an+k2an-1 where k∈(0,1) is a parameter, and let…Pavel Stovicek·Mar 10, 2022SaveLearn
Unwrapped two-point functions on high-dimensional toriWe study unwrapped two-point functions for the Ising model, the self-avoiding walk and a random-length loop-erased random walk on high-dimensional lattices with periodic boundary conditions. While…Youjin Deng, Timothy M. Garoni, Jens Grimm et al.·Mar 10, 2022SaveLearn
General Null Lagrangians and Their Novel Role in Classical DynamicsA method for constructing general null Lagrangians and their higher harmonics is presented for dynamical systems with one degree of freedom. It is shown that these Lagrangians can be used to obtain…Rupam Das, Zdzislaw E. Musielak·Mar 9, 2022SaveLearn
Projective geometry of homogeneous second order Hamiltonian operatorsWe prove the invariance of homogeneous second-order Hamiltonian operators under the action of projective reciprocal transformations. We establish a correspondence between such operators in dimension…Pierandrea Vergallo, Raffaele Vitolo·Mar 8, 2022SaveLearn
Graphene in complex magnetic fieldsExact analytic solutions for an electron in graphene interacting with external complex magnetic fields are found. The eigenvalue problem for the non-hermitian Dirac-Weyl Hamiltonian leads to a pair…DJ Fernández, JD García-Muñoz·Mar 8, 2022SaveLearn
Derivation of Kubo's formula for disordered systems at zero temperatureThis work justifies the linear response formula for the Hall conductance of a two-dimensional disordered system. The proof rests on controlling the dynamics associated with a random time-dependent…Wojciech De Roeck, Alexander Elgart, Martin Fraas·Mar 8, 2022SaveLearn
From Affine A4 to Affine H2: Group Theoretical Analysis of Five-fold TilingsThe projections of the lattices, may be used as models of quasicrystals, and the particular affine extension of the H2 symmetry as a subgroup of A4, discussed in the work, presents a different…Nazife Ozdes Koca, Ramazan Koc, Mehmet Koca et al.·Mar 8, 2022SaveLearn