相关论文: KMS states and complex multiplication
Complex potential transformations which add imaginary parts to chosen energy levels are given and qualitatively explained. Unexpected shape similarity of potential perturbations for real and imaginary E-shifts of bound states are exhibited.…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
Using the representation of the quantum group $SL_q$(2) by the Weyl ope\-ra\-tors of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal…
Let $C_c^{*}(\mathbb{N}^{2})$ be the universal $C^{*}$-algebra generated by a semigroup of isometries $\{v_{(m,n)}: m,n \in \mathbb{N}\}$ whose range projections commute. We analyse the structure of KMS states on $C_{c}^{*}(\mathbb{N}^2)$…
Quantum fields are considered as generators of infinite-dimensional Clifford algebra $Cl(\infty)$, which can be either orthogonal (in case of fermions) or symplectic (in case of bosons). A generic quantum state can be expressed as a…
The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations…
We consider a family of Cuntz-Pimsner algebras associated to self-similar group actions, and their Toeplitz analogues. Both families carry natural dynamics implemented by automorphic actions of the real line, and we investigate the…
On the example of a free massless and conformally coupled scalar field, it is argued that in quantum field theory in curved spacetimes with time-like Killing field, the corresponding KMS states (generalized Gibbs ensembles) at parameter…
We introduce a numerical approach to calculate the statistics of work done on 1D quantum lattice systems initially prepared in thermal equilibrium states. This approach is based on two tensor-network techniques: Time Evolving Block…
The manifestly Lorentz covariant formulation of quantum electrodynamics disregards Coulomb instantaneous interaction and its consequence - instantaneous bound states (IBS's). In this article we consider the way of construction the IBS…
Within the framework of relativistic quantum field theory, a novel method is established which allows to distinguish non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with…
We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each $\beta\in[1,2]$, there is a unique KMS$_\beta$ state, and we…
It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from the periodicity properties of the corresponding quantum monodromy. With the aim of…
We consider self-similar actions of groupoids on the path spaces of finite directed graphs, and construct examples of such self-similar actions using a suitable notion of graph automaton. Self-similar groupoid actions have a Cuntz-Pimsner…
Spielberg has recently shown that Baumslag-Solitar groups associated to pairs of positive integers are quasi-lattice ordered in the sense of Nica. Thus they have tractable Toeplitz algebras. Each of these algebras carries a natural…
We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability…
We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$.…
We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In…
The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the…
In this paper, we study KMS states for the gauge actions on C${}^*$-algebras associated with self-similar sets whose branch points are finite. If the self-similar set does not contain any branch point, the Hutchinson measure gives the…