arXiv subjects

Yaroslav Volovich

Publications and source records attributed to Yaroslav Volovich.

7 recordsLinked to original sources

arXiv2006

Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics

We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (but discrete time!) dynamics is compatible with discrete energy levels.

quant-ph↗

arXiv2004

Energy Flow from Open to Closed Strings in a Toy Model of Rolling Tachyon

We study the toy model of interacting open and closed string tachyons which demonstrates some interesting properties of the unstable D-brane decay scenario. We compute a stress tensor of the system and study the energy and pressure dynamics. We show that the total energy of the system is conserved. We separate the stress tensor into two parts corresponding to open and closed strings and study the energy flow from open to closed strings. The two vacua of the system could be interpreted as corresponding to the unstable D-brane background and the open string tachyon vacuum. We study how for spatially homogenous solution interpolating between these two vacua the total energy of the open string dissipates to the closed string.

math-ph↗

arXiv2004

Interference as a statistical consequence of conjecture on time quant

We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical effect for deterministic particles, i.e. particles that have trajectories and obey deterministic dynamical equations, if one introduces a discrete time. As a demonstration of this concept we consider particle scattering on a screen with a slit. We study how resulting interference picture depends on the parameters of the model. The resulting interference picture has a nontrivial minimum-maximum distribution which vanishes, as the time discreteness parameter goes to zero. This picture is qualitatively the same as one obtained in quantum experiments. The picture includes some interesting nonclassical properties such as a 'black' region behind the center of the slit.

quant-ph↗

arXiv2003

Numerical Study of Nonlinear Equations with Infinite Number of Derivatives

We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation is of much interest in mathematical physics and applications, in particular in cosmology. Differential equation with infinite number of derivatives could be written as nonlinear integral equations. We perform numerical investigation of solutions of the equations. It is established that these equations have two different regimes of the solutions: interpolating and periodic. The critical value of the parameter q separating these regimes is found to be q^2=1.37. Convergence of iterative procedure for these equations is proved.

math-ph↗

arXiv2002

Discrete Time Leads to Quantum-Like Interference of Deterministic Particles

In this note we demonstrate that a quantum-like interference picture could appear as a statistical effect of interference of deterministic particles, i.e. particles that have trajectories and obey deterministic equations, if one introduces a discrete time. The nature of the resulting interference picture does not follow from the geometry of force field, but is strongly attached to the time discreetness parameter. As a demonstration of this concept we consider a scattering of charged particles on the charged screen with a single slit. The resulting interference picture has a nontrivial minimum-maximum distribution which vanishes as the time discreetness parameter goes to zero that could be interpreted as an analog of quantum decoherence.

quant-ph↗

arXiv2000

Bell's Theorem and Random Variables

Bell's theorem states that quantum correlation function of two spins can not be represented as an expectation value of two classical random variables. Spin is described in Bell's model by a single scalar random variable. We discuss another classical model of spin in which spin is described by a triple of classical random variables. It is shown that in this model the quantum correlation function can be represented as the expectation value of classical random variables. Implications of this result to the problem of local causality of quantum mechanics and relations with problems of moments are briefly mentioned.

quant-ph↗

arXiv2000

Interacting Stochastic Process and Renormalization Theory

A stochastic process with self-interaction as a model of quantum field theory is studied. We consider an Ornstein-Uhlenbeck stochastic process x(t) with interaction of the form x^{(α)}(t)^4, where $α$ indicates the fractional derivative. Using Bogoliubov's R-operation we investigate ultraviolet divergencies for the various parameters $α$. Ultraviolet properties of this one-dimensional model in the case $α=3/4$ are similar to those in the $ϕ^4_4$ theory but there are extra counterterms. It is shown that the model is two-loops renormalizable. For $5/8\leq α< 3/4$ the model has a finite number of divergent Feynman diagrams. In the case $α=2/3$ the model is similar to the $ϕ^4_3$ theory. If $0 \leq α< 5/8$ then the model does not have ultraviolet divergencies at all. Finally if $α> 3/4$ then the model is nonrenormalizable. This model can be used for a non-perturbative study of ultraviolet divergencies in quantum field theory and also in theory of phase transitions.

quant-ph↗