TY - JOUR
AB - Let 𝐹:ℤ2→ℤ be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes.
AU - Kalinin, Nikita
AU - Shkolnikov, Mikhail
ID - 8325
JF - Communications in Mathematical Physics
SN - 00103616
TI - Sandpile solitons via smoothing of superharmonic functions
ER -
TY - JOUR
AB - We analyse the canonical Bogoliubov free energy functional in three dimensions at low temperatures in the dilute limit. We prove existence of a first-order phase transition and, in the limit (Formula presented.), we determine the critical temperature to be (Formula presented.) to leading order. Here, (Formula presented.) is the critical temperature of the free Bose gas, ρ is the density of the gas and a is the scattering length of the pair-interaction potential V. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula in the limit (Formula presented.).
AU - Napiórkowski, Marcin M
AU - Reuvers, Robin
AU - Solovej, Jan
ID - 554
IS - 1
JF - Communications in Mathematical Physics
SN - 00103616
TI - The Bogoliubov free energy functional II: The dilute Limit
VL - 360
ER -
TY - JOUR
AB - We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m*. The value of m* is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain.
AU - Moser, Thomas
AU - Seiringer, Robert
ID - 741
IS - 1
JF - Communications in Mathematical Physics
SN - 00103616
TI - Stability of a fermionic N+1 particle system with point interactions
VL - 356
ER -
TY - JOUR
AB - The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.
AU - Bao, Zhigang
AU - Erdös, László
AU - Schnelli, Kevin
ID - 1207
IS - 3
JF - Communications in Mathematical Physics
SN - 00103616
TI - Local law of addition of random matrices on optimal scale
VL - 349
ER -