Related papers: Bost-Connes-Marcolli systems for Shimura varieties…
We present a criterion of consistency derived from the analogy between the partition function of a quantum field theory and that of a statistical system. Based on this we examine a new class of higher dimension operators that might act in…
We consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where $n$ is even. For these varieties, we construct smooth $p$-adic integral models for $s=1$ and regular $p$-adic integral models for $s=2$ and $s=3$ over…
The asymmetry properties of a state relative to some symmetry group specify how and to what extent the given symmetry is broken by the state. Characterizing these is found to be surprisingly useful for addressing a very common problem: to…
Classifying phases of local quantum systems is a general problem that includes special cases such as free fermions, commuting projectors, and others. An important distinction in this classification should be made between classifying…
The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological…
M-theoretic construction of N=2 gauge theories implies that the instanton partition function is expressed as the scalar product of coherent states (Whittaker states) in the Verma module of an appropriate two dimensional conformal field…
Fermions are fundamental particles which obey seemingly bizarre quantum-mechanical principles, yet constitute all the ordinary matter that we inhabit. As such, their study is heavily motivated from both fundamental and practical incentives.…
We concentrate our study on a recent process algebra - PALOMA - intended to capture interactions between spatially distributed agents, for example in collective adaptive systems. New agent-based semantic rules for deriving the underlying…
In quantum mechanics, we define the measuring system $M$ in a selective measurement by two conditions. Firstly, when we define the measured system $S$ as the system in which the non-selective measurement part acts, $M$ is independent from…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…
The paper is devoted to further development of the new approach in equilibrium statistical mechanics the basis of which was worked out in a series of articles by the author. The approach proceeds on the use of a hierarchy of equations for…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
Despite the obvious difference between fermions and bosons in their physical properties and statistical distributions, but we have to ask the following question. What is the form of statistical distribution for a system of quantum particles…
The Fisher-Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is probed then than calculating it only in the configuration and momentum spaces will not give a complete description for…
With the purpose to introduce a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we study three quantumness quantifiers for bipartite optical systems: one based on…
We discuss some recent results connected with the properties of temperature states of quantum disordered systems. This analysis falls within the natural framework of operator algebras. Among the results quoted here, we recall some ergodic…
A method for constructing coherent states (CS) of finite-level systems with a given angular momentum is proposed. To this end we generalize the known spin equation (SE) to an infinite-dimensional Fock space. The equation describes a special…
Vacua of two dimensional incompressible system, such as Fractional Quantum Hall system, are characterized by rational conformal field theory. We develop a method to express the wavefunctions of those systems in terms of chiral vertices. We…
In this continuation paper the theory is further extended to reveal the connection between its formal aparatus, dealing with microscopic quantities, and the formal aparatus of thermodynamics, related to macroscopic properties of large…
We find the structure of generators of norm continuous quantum Markov semigroups on B(h) that are symmetric with respect to the scalar product tr(\rho^{1/2}x\rho^{1/2}y) induced by a faithful normal invariant state invariant state \rho and…