Letters in Mathematical Physics最新文献

We consider a protocol for the two-time measurement of entropic observables in quantum open systems driven out of thermal equilibrium by coupling to several heat baths. We concentrate on the Markovian approximation of the time-evolution and relate the expected value of the so defined entropy variations with the well-known expression of entropy production due to Lebowitz and Spohn. We do so under the detailed balance condition and, as a byproduct, we show that the probabilities of outcomes of two-time measurements are given by a continuous time Markov process determined by the Lindblad generator of the Markovian quantum dynamics.

Any finite state automaton gives rise to a Boolean one-dimensional TQFT with defects and inner endpoints of cobordisms. This paper extends the correspondence to Boolean TQFTs where defects accumulate towards inner endpoints, relating such TQFTs and topological theories to sofic systems and (omega )-automata.

In this short note, we explain that Huisken’s isoperimetric mass is always nonnegative for elementary reasons.

We construct a homomorphism from the affine Yangian (Y_{hbar ,varepsilon +hbar }(widehat{mathfrak {sl}}(n))) to the affine Yangian (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n+1))) which is different from the one in Ueda (A homomorphism from the affine Yangian (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n))) to the affine Yangian (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n+1))), 2023. arXiv:2312.09933). By using this homomorphism, we give a homomorphism from (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n))otimes Y_{hbar ,varepsilon +nhbar }(widehat{mathfrak {sl}}(m))) to (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(m+n))). As an application, we construct a homomorphism from the affine Yangian (Y_{hbar ,varepsilon +nhbar }(widehat{mathfrak {sl}}(m))) to the centralizer algebra of the pair of affine Lie algebras ((widehat{mathfrak {gl}}(m+n),widehat{mathfrak {sl}}(n))) and the coset vertex algebra of the pair of rectangular W-algebras (mathcal {W}^k(mathfrak {gl}(2m+2n),(2^{m+n}))) and (mathcal {W}^{k+m}(mathfrak {sl}(2n),(2^{n}))).

We consider ground states of the N coupled fermionic nonlinear Schrödinger systems with the Coulomb potential V(x) in the (L^2)-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter (alpha >0), which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as (alpha rightarrow infty ), where the mass concentrates at one of the singular points for the Coulomb potential V(x).

The notion of a quantum tau-function for a natural quantization of the KdV hierarchy was introduced in a work of Dubrovin, Guéré, Rossi, and the second author. A certain natural choice of a quantum tau-function was then described by the first author, the coefficients of the logarithm of this series are called the quantum intersection numbers. Because of the Kontsevich–Witten theorem, a part of the quantum intersection numbers coincides with the classical intersection numbers of psi-classes on the moduli spaces of stable algebraic curves. In this paper, we relate the quantum intersection numbers to the stationary relative Gromov–Witten invariants of (({{{mathbb {C}}}{{mathbb {P}}}}^1,0,infty )) with an insertion of a Hodge class. Using the Okounkov–Pandharipande approach to such invariants (with the trivial Hodge class) through the infinite wedge formalism, we then give a short proof of an explicit formula for the “purely quantum” part of the quantum intersection numbers, found by the first author, which in particular relates these numbers to the one-part double Hurwitz numbers.

We provide an operator-algebraic construction of integrable models of quantum field theory on 1+1-dimensional Minkowski space with fermionic scattering states. These are obtained by a grading of the wedge-local fields or, alternatively, of the underlying Borchers triple defining the theory. This leads to a net of graded-local field algebras, of which the even part can be considered observable, although it is lacking Haag duality. Importantly, the nuclearity condition implying nontriviality of the local field algebras is independent of the grading, so that existing results on this technical question can be utilized. Application of Haag–Ruelle scattering theory confirms that the asymptotic particles are indeed fermionic. We also discuss connections with the form factor programme.

In the present paper, we study the weakly periodic p-adic quasi-Gibbs measures for the three-state Potts model on a Cayley tree of order two. Under some conditions, we show there exist 14 weakly periodic (non-periodic) p-adic quasi-Gibbs measures. Moreover, if (p=3) then there are six weakly periodic p-adic Gibbs measures for this model. We also prove that if (pne 3) then a phase transition occurs for the Potts model on a Cayley tree of order two.

We construct a class of fixed-time models in which the commutations relations of a Dirac field with a bosonic field are non-trivial and depend on the choice of a given distribution (“twisting factor”). If the twisting factor is fundamental solution of a differential operator, then applying the differential operator to the bosonic field yields a generator of the local gauge transformations of the Dirac field. Charged vectors generated by the Dirac field define states of the bosonic field which in general are not local excitations of the given reference state. The Hamiltonian density of the bosonic field presents a non-trivial interaction term: besides creating and annihilating bosons, it acts on momenta of fermionic wave functions. When the twisting factor is the Coulomb potential, the bosonic field contributes to the divergence of an electric field and its Laplacian generates local gauge transformations of the Dirac field. In this way, we get a fixed-time model fulfilling the equal time commutation relations of the interacting Coulomb gauge.

The Kerr-star spacetime is the extension over the horizons and in the negative radial region of the slowly rotating Kerr black hole. It is known that below the inner horizon, there exist both timelike and null (lightlike) closed curves. Nevertheless, we prove that null geodesics can be neither closed nor even contained in a compact subset of the Kerr-star spacetime.