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The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear…
All the laws of physics are time-reversible. Time arrow emerges only when ensembles of classical particles are treated probabilistically, outside of physics laws, and the entropy and the second law of thermodynamics are introduced. In…
Covariant phase space quantization attempts to quantize the full space of classical solutions, leading to a quantum theory in which the usual time coordinate is missing. In this paper we explore how the time evolution of the quantum states…
The dynamics of non-polar diatomic molecules interacting with a far-detuned narrow-band laser field, that only may drive rotational transitions, is studied. The rotation of the molecule is considered both classically and quantum…
Despite being created through a fundamentally quantum-mechanical process, cosmological structures have not yet revealed any sign of genuine quantum correlations. Among the obstructions to the direct detection of quantum signatures in…
A mesoscopic evolution equation for an ensemble of mesoparticles follows after the elimination of internal degrees of freedom. If the system is composed of a hierarchy of scales, the reduction procedure could be worked repeatedly and the…
The possible imprint of quantum decoherence, in the framework of cosmology, is here investigated. Particular attention is paid to the observational fact that entanglement could lead to the interaction of different eras of cosmic evolution.…
An initial local excitation in a confined quantum system evolves exploring the whole system, returning to the initial position as a mesoscopic echo at the Heisenberg time. We consider a two weakly coupled spin chains, a spin ladder, where…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
The theory of inverse spectra of $T_0$ Alexandroff topological spaces is used to construct a model of $T_0$-discrete four-dimensional spacetime. The universe evolution is interpreted in terms of a sequence of topology changes in the set of…
To incorporate quantum nonlocality into general relativity, we propose that the preparation and measurement of a quantum system are simultaneous events. To make progress in realizing this proposal, we introduce a spacetime geometry that is…
We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for…
Classically, one could imagine a completely static space, thus without time. As is known, this picture is unconceivable in quantum physics due to vacuum fluctuations. The fundamental difference between the two frameworks is that classical…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
The problem of topology change description in gravitation theory is analized in detailes. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of boundary conditions (or…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder…
We investigate the emergence of quantum coherence and quantum correlations in a two-particle system with deformed symmetries arising from the quantum nature of spacetime. We demonstrate that the deformation of energy-momentum composition…