TY - JOUR AB - Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail. AU - Runkel, Ingo AU - Szegedy, Lorant ID - 8816 IS - 1 JF - Communications in Mathematical Physics SN - 00103616 TI - Area-dependent quantum field theory VL - 381 ER - 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 IS - 9 JF - Communications in Mathematical Physics SN - 00103616 TI - Sandpile solitons via smoothing of superharmonic functions VL - 378 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 - 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 - 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 -