TY - JOUR AB - We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with L-body interactions, where L is the number of spins. This mathematically verifies the observation first made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130) that the ETH may hold for systems with additional translational symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interaction. AU - Sugimoto, Shoki AU - Henheik, Sven Joscha AU - Riabov, Volodymyr AU - Erdös, László ID - 13317 IS - 7 JF - Journal of Statistical Physics SN - 0022-4715 TI - Eigenstate thermalisation hypothesis for translation invariant spin systems VL - 190 ER - TY - JOUR AB - We study the many-body dynamics of an initially factorized bosonic wave function in the mean-field regime. We prove large deviation estimates for the fluctuations around the condensate. We derive an upper bound extending a recent result to more general interactions. Furthermore, we derive a new lower bound which agrees with the upper bound in leading order. AU - Rademacher, Simone Anna Elvira AU - Seiringer, Robert ID - 11917 JF - Journal of Statistical Physics KW - Mathematical Physics KW - Statistical and Nonlinear Physics SN - 0022-4715 TI - Large deviation estimates for weakly interacting bosons VL - 188 ER - TY - JOUR AB - We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature. AU - Henheik, Sven Joscha AU - Lauritsen, Asbjørn Bækgaard ID - 11732 JF - Journal of Statistical Physics KW - Mathematical Physics KW - Statistical and Nonlinear Physics SN - 0022-4715 TI - The BCS energy gap at high density VL - 189 ER - TY - JOUR AB - We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass. AU - Mysliwy, Krzysztof AU - Seiringer, Robert ID - 10564 IS - 1 JF - Journal of Statistical Physics SN - 0022-4715 TI - Polaron models with regular interactions at strong coupling VL - 186 ER - TY - JOUR AB - In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of N d-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N−1)−1Ndβv(Nβ·)forβ∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN)-norm to arbitrary precision in powers of N−1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution. AU - Bossmann, Lea AU - Pavlović, Nataša AU - Pickl, Peter AU - Soffer, Avy ID - 7508 JF - Journal of Statistical Physics SN - 0022-4715 TI - Higher order corrections to the mean-field description of the dynamics of interacting bosons VL - 178 ER - TY - JOUR AB - We consider the Fröhlich model of a polaron, and show that its effective mass diverges in thestrong coupling limit. AU - Lieb, Elliott H. AU - Seiringer, Robert ID - 7235 JF - Journal of Statistical Physics SN - 0022-4715 TI - Divergence of the effective mass of a polaron in the strong coupling limit VL - 180 ER - TY - JOUR AB - We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor. AU - Baity-Jesi, Marco AU - Goodrich, Carl Peter AU - Liu, Andrea J. AU - Nagel, Sidney R. AU - Sethna, James P. ID - 7756 IS - 3-4 JF - Journal of Statistical Physics SN - 0022-4715 TI - Emergent SO(3) symmetry of the frictionless shear jamming transition VL - 167 ER - TY - JOUR AB - We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear Boltzmann equation globally in time. The collision kernel is identified as the sum of an emission and an absorption term that depend on the equilibrium distribution of the free phonon modes. AU - Erdös, László ID - 2738 IS - 5-6 JF - Journal of Statistical Physics SN - 0022-4715 TI - Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field VL - 107 ER - TY - JOUR AB - We consider a quantum particle moving in a harmonic exterior potential and linearly coupled to a heat bath of quantum oscillators. Caldeira and Leggett derived the Fokker Planck equation with friction for the Wigner distribution of the particle in the large-temperature limit: however, their (nonrigorous) derivation was not free of criticism, especially since the limiting equation is not of Lindblad form. In this paper we recover the correct form of their result in a rigorous way. We also point out that the source of the diffusion is physically restrictive under this scaling. We investigate the model at a fixed temperature and in the large-time limit, where the origin of the diffusion is a cumulative effect of many resonant collisions. We obtain a heat equation with a friction term for the radial process in phase space and we prove the Einstein relation in this case. AU - Castella, François AU - Erdös, László AU - Frommlet, Florian AU - Markowich, Peter ID - 2732 IS - 3-4 JF - Journal of Statistical Physics SN - 0022-4715 TI - Fokker-Planck equations as scaling limits of reversible quantum systems VL - 100 ER - TY - JOUR AB - We consider a multidimensional system consisting of a particle of mass M and radius r (molecule), surrounded by an infinite ideal gas of point particles of mass m (atoms). The molecule is confined to the unit ball and interacts with its boundary (barrier) via elastic collision, while the atoms are not affected by the boundary. We obtain convergence to equilibrium for the molecule from almost every initial distribution on its position and velocity. Furthermore, we prove that the infinite composite system of the molecule and the atoms is Bernoulli. AU - Erdös, László AU - Tuyen, Dao ID - 2721 IS - 5-6 JF - Journal of Statistical Physics SN - 0022-4715 TI - Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier VL - 59 ER -