Related papers: Bost-Connes-Marcolli systems for Shimura varieties…
The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations…
Gibbs states are known to play a crucial role in the statistical description of a system with a large number of degrees of freedom. They are expected to be vital also in a quantum gravitational system with many underlying fundamental…
Coherent states provide an appealing method to reconstruct efficiently a pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s+1) expectations of projection operators on appropriate coherent states in…
Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue. In this paper, we develop a novel statistical higher-order…
Norm-compatible families of cohomology classes for Shimura varieties, and other arithmetic symmetric spaces, play an important role in Iwasawa theory of automorphic forms. The aim of this note is to give a systematic approach to proving…
A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite…
Statistical mechanics for states with complex eigenvalues, which are described by Gel'fand triplet and represent unstable states like resonances, are discussed on the basis of principle of equal ${\it a priori}$ probability. A new entropy…
Continuing the analysis in a unified scheme for treating generalized superselection sectors based upon the notion of selection criteria for states of relevance in quantum physics, we extend the Doplicher-Roberts superselection theory for…
Since symmetry properties of coherent states (CS) on M\"obius strip (MS) and fermions are closely related, CS on MS are naturally associated to the topological properties of fermionic fields. Here we consider CS and superpositions of…
Starting from the equations of motion of the fields involved in a theory with spontaneous symmetry breaking and by making simple assumptions regarding their behavior we derive simple tree level relations between the mass of the Higgs boson…
We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson…
The result that closed systems evolve toward equilibrium is derived entirely on the basis of quantum field theory for a model system, without invoking any of the common extra-mathematical notions of particle trajectories, collapse of the…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
We introduce "quantum barcodes," a theoretical framework that applies persistent homology to classify topological phases in quantum many-body systems. By mapping quantum states to classical data points through strategic observable…
We analyze the phenomena of spontaneous symmetry breaking in Quantum Finance by using as a starting point the Black-Scholes (BS) and the Merton-Garman (MG) equations expressed in the Hamiltonian form. In this scenario the martingale…
A fundamental pillar of quantum mechanics concerns indistinguishable quantum particles. In three dimensions they may be classified into fermions or bosons, having, respectively, antisymmetric or symmetric wave functions under particle…
Double layer quantum Hall systems have interesting properties associated with interlayer correlations. At $\nu =1/m$ where $m$ is an odd integer they exhibit spontaneous symmetry breaking equivalent to that of spin $1/2$ easy-plane…
Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her…
We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous…
We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus…