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The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
We explore the extended framework of the generalized quantum mechanics and discuss various aspects of neighborhood in the construction of space in search of origin of cosmological constant. We propose to expand definition of the volume of…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
We examine the medium time quantum dynamics and population equilibration of two, three and four-well Bose-Hubbard models using stochastic integration in the truncated Wigner phase-space representation. We find that all three systems will…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
The phase transition kinetics in three phase systems was investigated using the numerically efficient cell dynamics method. A phasefield model with a simple analytical free energy and single order parameter was used to study the kinetics…
We experimentally demonstrate the strictly nonclassical behavior in a many-atom system using a recently derived criterion [E. Kot et al., Phys. Rev. Lett. 108, 233601 (2012)] that explicitly does not make use of quantum mechanics. We…
We introduce a simple model of a growing system with $m$ competing communities. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical…
We investigate a real scalar field whose dynamics is governed by a nonlinear wave equation. We show that classical description can be applied to a quantum system of many interacting bosons provided that some quantum ingredients are…
We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge,…
A generic kind of quantum chaotic ratchet is introduced, based on initial states that are \emph{uniform} in phase space with the \emph{maximal possible} resolution of one Planck cell. Unlike a classical phase-space uniform density, such a…
In order to study the validity of analytical formulas used in the calculation of characteristic physical quantities related to vacuum bubbles, we conduct several numerical simulations of bubble kinematics in the context of cosmological…
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy…
A thermodynamic system of non-interacting quantum particles changes its statistical distribution formulas if there is a universal limitation for the size of energetic quantum leaps (magnitude of quantum leaps smaller than Planck energy). By…
We review the formalism by which the tunnelling probability of an unstable ground state can be computed in quantum field theory, with special reference to the Standard Model of electroweak interactions. We describe in some detail the…
We discuss a scenario of ``the path to physics at the Planck scale'' where todays theory of the interactions of elementary particles, the so called Standard Model (SM), emerges as a low energy effective theory describing the long distance…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
Scale invariance supplemented by the requirement of the absence of new heavy particles may play an important role in addressing the hierarchy problem. We discuss how the Standard Model may become scale invariant at the quantum level above a…
Recently, a correspondence has been shown to exist between the structure of a single Standard Model generation of elementary particles and the properties of the Clifford algebra of nonrelativistic phase space. Here, this correspondence is…
A fundamental spacetime scale in the universe leads to noncommutative spacetime and thence to a modified energy - momentum dispersion relation or equivalently to a modification of Lorentz symmetry as shown by the author and others. This…