Related papers: Higher time derivatives, stability and Fermi Stati…
Starting from the old idea that Fermi statistics for quarks play a fundamental role to explain some features of hadron structure, we study the modification of the scaling behaviour of parton distributions due to quantum statistical effects.…
In a previous paper we began our analysis on the role of non self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growing interest on this topic and on some recent results on…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
A new kind of quantum statistics which interpolates between Bose and Fermi statistics is proposed beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles. The…
We discuss exactly solvable systems involving integrals of motion with higher powers of momenta. If one of these integrals is chosen for the Hamiltonian, we obtain a higher-derivative system involving ghosts, i.e. a system whose Hamiltonian…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
As time is not an observable, we use Fisher information (FI) to address the problem of time. We show that the Hamiltonian constraint operator cannot be used to analyze any quantum process for quantum geometries that are associated with…
After reviewing the description of an unstable state in the framework of Lee Hamiltonians (valid both for Quantum Mechanics (QM) and Quantum Field Theory (QFT)), we consider some theoretical aspects of non-exponential decays: the case of…
We present a new understanding of the unstable ghost-like resonance which appears in theories such as quadratic gravity and Lee-Wick type theories. Quantum corrections make this resonance unstable, such that it does not appear in the…
In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are…
Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems…
We address a simple connection between results of Hamiltonian nonlinear dynamical theory and thermostatistics. Using a properly defined dynamical temperature in low-dimensional symplectic maps, we display and characterize long-standing…
Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…
Quantum effects arising from manifestly broken time-reversal symmetry are investigated using time-dependent perturbation theory in a simple model. The forward time and the backward time Hamiltonians are taken to be different and hence the…
The stability of a Fermi liquid is analyzed by summing series of diagrams with an interaction mediated by a system close to quantum criticality. The critical temperature and the gap are derived in terms of an effective coupling constant and…
In relativistic quantum field theory particles of half-integer spin must obey Fermi-Dirac statistics. Their quantum operators must anticommute at spacelike separation in contrast to commuting physical observables. We show that Fermi-Dirac…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
A quantum statistical system with energy dissipation is studied. Its statisitics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble. The eigenenergies are shown to form stable structure in…
We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that break discrete time translation symmetry in driven quantum many-body systems…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…