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I. V. Volovich

Publications and source records attributed to I. V. Volovich.

At least 37 records · Page 2Linked to original sources
arXiv2011

Cosmological Daemon

Classical versions of the Big Bang cosmological models of the universe contain a singularity at the start of time, hence the time variable in the field equations should run over a half-line. Nonlocal string field theory equations with infinite number of derivatives are considered and an important difference between nonlocal operators on the whole real line and on a half-line is pointed out. We use the heat equation method and show that on the half-line in addition to the usual initial data a new arbitrary function (external source) occurs that we call the daemon function. The daemon function governs the evolution of the universe similar to Maxwell`s demon in thermodynamics. The universe and multiverse are open systems interacting with the daemon environment. In the simplest case the nonlocal scalar field reduces to the usual local scalar field coupled with an external source which is discussed in the stochastic approach to inflation. The daemon source can help to get the chaotic inflation scenario with a small scalar field.

hep-th↗
arXiv2010

The Arrhenius formula in kinetic theory and Witten's spectral asymptotics

A new approach to the proof of the Arrhenius formula of kinetic theory is proposed. We prove this formula starting from the equation of diffusion in a potential. We put this diffusion equation in the form of evolutionary equation generated by some Schroedinger operator. We show that the Arrhenius formula for the rate of over the barrier transitions follows from the formula for the rate of quantum tunnel transitions for the considered Schroedinger operator. Relation of the proposed approach and the Witten method of the proof of the Morse inequalities is discussed. In our approach the Witten spectral asymptotics takes the form of the low temperature limit and the Arrhenius formula is a correction to the Witten asymptotics.

math-ph↗
arXiv2009

Functional Classical Mechanics and Rational Numbers

The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since arbitrary real numbers are unobservable. This notion leads to the known paradoxes, such as the irreversibility problem. A "functional" formulation of classical mechanics is suggested. The physical meaning is attached in this formulation not to an individual trajectory but only to a "beam" of trajectories, or the distribution function on phase space. The fundamental equation of the microscopic dynamics in the functional approach is not the Newton equation but the Liouville equation for the distribution function of the single particle. The Newton equation in this approach appears as an approximate equation describing the dynamics of the average values and there are corrections to the Newton trajectories. We give a construction of probability density function starting from the directly observable quantities, i.e., the results of measurements, which are rational numbers.

math-ph↗
arXiv2009

On Solutions to the Wave Equation on Non-globally Hyperbolic Manifold

We consider the Cauchy problem for the wave equation on a non-globally hyperbolic manifold of the special form (Minkowski plane with a handle) containing closed timelike curves (time machines). We prove that the classical solution of the Cauchy problem exists and is unique if and only if the initial data satisfy to some set of additional conditions.

math-ph↗
arXiv2009

Cauchy Problem on Non-globally Hyperbolic Spacetimes

Solutions of the Cauchy problem for the wave equation on a non-globally hyperbolic spacetime, which contains closed timelike curves (time machines) are considered. It is proved, that there exists a solution of the Cauchy problem, it is discontinuous and in some sense unique for arbitrary initial conditions, which are given on a hypersurface at time, that precedes the formation of closed timelike curves (CTC). If the hypersurface of initial conditions intersects the region containing CTC, then the solution of the Cauchy problem exists only for such initial conditions, that satisfy a certain requirement of self-consistency.

hep-th↗
arXiv2007

Time Machine at the LHC

Recently, black hole and brane production at CERN's Large Hadron Collider (LHC) has been widely discussed. We suggest that there is a possibility to test causality at the LHC. We argue that if the scale of quantum gravity is of the order of few TeVs, proton-proton collisions at the LHC could lead to the formation of time machines (spacetime regions with closed timelike curves) which violate causality. One model for the time machine is a traversable wormhole. We argue that the traversable wormhole production cross section at the LHC is of the same order as the cross section for the black hole production. Traversable wormholes assume violation of the null energy condition (NEC) and an exotic matter similar to the dark energy is required. Decay of the wormholes/time machines and signatures of time machine events at the LHC are discussed.

hep-ph↗
arXiv2007

Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.

hep-th↗
arXiv2006

Mass Spectrum, Actons and Cosmological Landscape

It is suggested that the properties of the mass spectrum of elementary particles could be related with cosmology. Solutions of the Klein-Gordon equation on the Friedmann type manifold with the finite action are constructed. These solutions (actons) have a discrete mass spectrum. We suggest that such solutions could select a universe from cosmological landscape. In particular the solutions with the finite action on de Sitter space are investigated.

hep-th↗
arXiv2006

On the Null Energy Condition and Cosmology

Field theories which violate the null energy condition (NEC) are of interest for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter $w<-1$. We discuss the consistency of two recently proposed models that violate the NEC. The ghost condensate model requires higher-order derivative terms in the action. It leads to a heavy ghost field and unbounded energy. We estimate the rates of particles decay and discuss possible mass limitations to protect stability of matter in the ghost condensate model. The nonlocal stringy model that arises from a cubic string field theory and exhibits a phantom behavior also leads to unbounded energy. In this case the spectrum of energy is continuous and there are no particle like excitations. This model admits a natural UV completion since it comes from superstring theory.

hep-th↗
arXiv2006

Renormalization of Quantum Electrodynamics and Hopf Algebras

In 1999, A. Connes and D. Kreimer have discovered the Hopf algebra structure on the Feynman graphs of scalar field theory. They have found that the renormalization can be interpreted as a solving of some Riemann -- Hilbert problem. In this work a generalization of their scheme to the case of quantum electrodynamics is proposed. The action of the gauge group on the Hopf algebra of diagrams are defined and the proof that this action is consistent with the Hopf algebra structure is given.

hep-th↗
arXiv2006

On Standards and Specifications in Quantum Cryptography

Quantum cryptography is going to find practically useful applications. Recently some first quantum cryptographic solutions became available on the market. For clients it is important to be able to compare the quality and properties of the proposed products. To this end one needs to elaborate on specifications and standards of solutions in quantum cryptography. We propose and discuss a list of characteristics for the specification, which includes numerical evaluations of the security of solution and can be considered as a standard for quantum key distribution solutions. The list is based on the average time of key generation depending on some parameters. In the simplest case for the user the list includes three characteristics: the security degree, the length of keys and the key refresh rate.

quant-ph↗
arXiv2006

Finite Action Klein-Gordon Solutions on Lorentzian Manifolds

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this note we consider such a problem for the hyperbolic Klein-Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein-Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.

gr-qc↗
arXiv2005

Role of Various Entropies in the Black Hole Information Loss Problem

In a recent paper Hawking has argued that there is no information loss in black holes in asymptotically AdS spacetimes. We remind that there are several types of information (entropy) in statistical physics -- fine grained (microscopic) and coarse grained (macroscopic) ones which behave differently under unitary evolution. We suggest that the coarse grained information of the rest of the Universe is lost while fine grained information is preserved. A possibility to develop in quantum gravity an analogue of the Bogoliubov derivation of the irreversible Boltzmann and Navier - Stokes equations from the reversible mechanical equations is discussed.

hep-th↗
arXiv2005

General model of quantum key distribution

A general mathematical framework for quantum key distribution based on the concepts of quantum channel and Turing machine is suggested. The security for its special case is proved. The assumption is that the adversary can perform only individual (in essence, classical) attacks. For this case an advantage of quantum key distribution over classical one is shown.

quant-ph↗
arXiv2003

Quantum Multipole Noise and Generalized Quantum Stochastic Equations

A notion of quantum multipole (in particular, dipole) noise is considered. Quantum dipole noise is an analogue of quantum white noise but it acts in a Fock space with indefinite metric. Quantum {\it white} noise describes the leading term in the stochastic limit approximation to quantum dynamics while quantum {\it multipole} noise describes the corrections to the leading term. We obtain and study the generalized quantum stochastic equations describing corrections to the stochastic limit which include quantum dipole noise.

math-ph↗
arXiv2002

String Model with Dynamical Geometry and Torsion

A string model with dynamical metric and torsion is proposed. The geometry of the string is described by an effective Lagrangian for the scalar and vector fields. The path integral quantization of the string is considered.

hep-th↗
arXiv2002

Quantum stochastic equation for the low density limit

A new derivation of quantum stochastic differential equation for the evolution operator in the low density limit is presented. We use the distribution approach and derive a new algebra for quadratic master fields in the low density limit by using the energy representation. We formulate the stochastic golden rule in the low density limit case for a system coupling with Bose field via quadratic interaction. In particular the vacuum expectation value of the evolution operator is computed and its exponential decay is shown.

quant-ph↗