Exponential Control of Excitations for Trapped BEC in the Gross-Pitaevskii RegimeWe consider trapped Bose gases in three dimensions in the Gross-Pitaevskii regime whose low energy states are well known to exhibit Bose-Einstein condensation. That is, the majority of the particles…Nils Behrmann, Christian Brennecke, Simone Rademacher·Jan 27, 2025SaveLearn
Z2\ × Z2-graded Lie (super)algebras and generalized quantum statisticsWe present systems of parabosons and parafermions in the context of Lie algebras, Lie superalgebras, Z2\ × Z2-graded Lie algebras and $ Z2\…N. I. Stoilova, J. Van der Jeugt·Jan 26, 2025SaveLearn
Bulk-edge correspondence in finite photonic structureIn this work, we establish the bulk-edge correspondence principle for finite two-dimensional photonic structures. Specifically, we focus on the divergence-form operator with periodic coefficients and…Jiayu Qiu, Hai Zhang·Jan 26, 2025SaveLearn
e-product of distributions, with applicationsWe consider and reformulate a recent definition of multiplication between distributions. We show that this definition can be adopted, in particular, to prove biorthonormality of some distributions…Fabio Bagarello·Jan 25, 2025SaveLearn
Generalized theta series and monodromy of Casimir connection. The case of rank 1The monodromy of the (2) Casimir connection is considered. It is shown that the trace of the monodromy operator over the appropriate space of flat sections gives rise to the Jacobi theta…Egor Dotsenko·Jan 25, 2025SaveLearn
Mean-field limit from general mixtures of experts to quantum neural networksIn this work, we study the asymptotic behavior of Mixture of Experts (MoE) trained via gradient flow on supervised learning problems. Our main result establishes the propagation of chaos for a MoE as…Anderson Melchor Hernandez, Davide Pastorello, Giacomo De Palma·Jan 24, 2025SaveLearn
Thomas-Wigner rotation via Clifford algebrasWe derive Macfarlane's formula for the Thomas-Wigner angle of rotation using Clifford-algebra methods. The presentation is pedagogical and elementary, suitable for students with some basic knowledge…Piotr T. Chruściel, Helmuth Urbantke·Jan 24, 2025SaveLearn
A Classifying Space for Phases of Matrix Product StatesWe construct a topological space B consisting of translation invariant injective matrix product states (MPS) of all physical and bond dimensions and show that it has the weak homotopy…Daniel D. Spiegel, Marvin Qi, David T. Stephen et al.·Jan 24, 2025SaveLearn
v-representability and Hohenberg-Kohn theorem for non-interacting Schr\"odinger operators with distributional potentials in the one-dimensional torusIn this paper, we show that the ground-state density of any non-interacting Schr\"odinger operator on the one-dimensional torus with potentials in a certain class of distributions is strictly…Thiago Carvalho Corso·Jan 23, 2025SaveLearn
Edge spectrum for truncated Z2-insulatorsFermionic time-reversal-invariant insulators in two dimensions -- class AII in the Kitaev table -- come in two different topological phases. These are characterized by a Z2-index: the…Alexis Drouot, Jacob Shapiro, Xiaowen Zhu·Jan 22, 2025SaveLearn
Euler--Poincar\'e reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamicsThe Euler--Poincar\'e equations, firstly introduced by Henri Poincar\'e in 1901, arise from the application of Lagrangian mechanics to systems on Lie groups that exhibit symmetries, particularly in…Yusuke Ono, Simone Fiori, Linyu Peng·Jan 22, 2025SaveLearn
Achronal localization and representation of the causal logic from a conserved current, application to the massive scalar bosonOnly recently the concept of achronal localization has been developed as the adequate frame for the description of the localizability of a relativistic quantum mechanical system. Here covariant…Domenico P. L. Castrigiano, Carmine De Rosa, Valter Moretti·Jan 22, 2025SaveLearn
The multiplicative constant in asymptotics of higher-order analogues of the Tracy-Widom distributionIn this paper, we are concerned with higher-order analogues of the Tracy-Widom distribution, which describe the eigenvalue distributions in unitary random matrix models near critical edge points. The…Dan Dai, Wen-Gao Long, Shuai-Xia Xu et al.·Jan 22, 2025SaveLearn
The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transitionWe deal with a type I superconductor in a constant external magnetic field. We obtain the BCS-Bogoliubov gap equation with external magnetic field and apply the implicit function theorem to it. We…Shuji Watanabe·Jan 22, 2025SaveLearn
Link in RP3 and the Topological VertexWe provide the first computations of colored unknots and Hopf link in RP3 using both the topological vertex and its refinement. Our approach utilizes the toric Calabi-Yau…John Chae·Jan 22, 2025SaveLearn
Density matrices and entropy operator for non-Hermitian quantum mechanicsIn this paper we consider density matrices operator related to non-Hermitian Hamiltonians. In particular, we analyse two natural extensions of what is usually called a density matrix operator (DM),…Fabio Bagarello, Francesco Gargano, Lidia Saluto·Jan 20, 2025SaveLearn
Localized stem structures in soliton reconnection of the asymmetric Nizhnik-Novikov-Veselov systemThe reconnection processes of 3-solitons with 2-resonance can produce distinct local structures that initially connect two pairs of V-shaped branches, then disappear, and later re-emerge as new…Feng Yuan, Jingsong He, Yi Cheng·Jan 20, 2025SaveLearn
Localization of the massive scalar boson on achronal hyperplanes, derivation of Lorentz contractionIt is shown that the causal localizations of the massive scalar boson on spacelike hyperplanes extend uniquely to all achronal hyperplanes. The extension occurs by means of the high boost limit in a…Domenico P. L. Castrigiano·Jan 19, 2025SaveLearn
A dynamical systems approach to WKB-methods: The eigenvalue problem for a single well potentialIn this paper, we revisit the eigenvalue problem of the one-dimensional Schr\"odinger equation for smooth single well potentials. In particular, we provide a new interpretation of the…Kristian Uldall Kristiansen, Peter Szmolyan·Jan 18, 2025SaveLearn
Two-sided bounds on the point-wise spatial decay of ground states in the renormalized Nelson model with confining potentialsWe study the renormalized Nelson model for a scalar matter particle in a continuous confining potential interacting with a possibly massless quantized radiation field. When the radiation field is…Fumio Hiroshima, Oliver Matte·Jan 18, 2025SaveLearn
Determination of period matrix of double of surface with boundary via its DN mapAs is well-known, a conformal class of a surface M with boundary is determined by its DN map . In the paper, the algorithm for determination of the b-period matrix B…Dmitrii Korikov·Jan 17, 2025SaveLearn
Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elementsWe consider a particular class of sesquilinear forms on a Banach quasi *-algebra ([\|.\|],[\|.\|0]) which we call eigenstates of an element a∈, and we deduce some of their…Fabio Bagarello, Hiroshi Inoue, Salvatore Triolo·Jan 17, 2025SaveLearn
The q-Racah polynomials from scalar products of Bethe states IIThe theory of Leonard triples is applied to the derivation of normalized scalar products of on-shell and off-shell Bethe states generated from a Leonard pair. The scalar products take the form of…Pascal Baseilhac, Rodrigo A. Pimenta·Jan 17, 2025SaveLearn
Quantum tomography from the evolution of a single expectationWe investigate the possibility of performing full quantum tomography based on the homogeneous time evolution of a single expectation value. Remarkably, every non-trivial binary measurement evolved by…Hjalmar Rall, Michael M. Wolf·Jan 17, 2025SaveLearn
Stability of the π-Flux Phase for Z2 Lattice Gauge Theory Coupled to Fermionic MatterWe consider the two-dimensional Z2 Ising gauge theory coupled to fermionic matter. In absence of electric fields, we prove that, at half-filling, the ground state of the gauge theory…Leonardo Goller, Marcello Porta·Jan 17, 2025SaveLearn