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Igor Volovich

Publications and source records attributed to Igor Volovich.

31 records · Page 2Linked to original sources
arXiv2019

Revealing nonperturbative effects in the SYK model

We study the large $N$ saddle points of two SYK chains coupled by an interaction that is nonlocal in Euclidean time. We start from analytic treatment of the free case with $q=2$ and perform the numerical study of the interacting case $q=4$. We show that in both cases there is a nontrivial phase structure with infinite number of phases. Every phase correspond to a saddle point in the non-interacting two-replica SYK. The nontrivial saddle points have non-zero value of the replica-nondiagonal correlator in the sense of quasi-averaging, when the coupling between replicas is turned off. Thus, the nonlocal interaction between replicas provides a protocol for turning the nonperturbatively subleading effects in SYK into non-equilibrium configurations which dominate at large $N$. For comparison we also study two SYK chains with local interaction for $q=2$ and $q=4$. We show that the $q=2$ model also has a similar phase structure, whereas in the $q=4$ model, dual to the traversable wormhole, the phase structure is different.

hep-th↗
arXiv2019

Spontaneous symmetry breaking in fermionic random matrix model

A fermionic random matrix model, which is a 0-dimensional version of the SYK model with replicas, is considered. The replica-off-diagonal correlation functions vanish at finite N, but we show that they do not vanish in the large N limit due to spontaneous symmetry breaking. We use the Bogoliubov quasi-averages approach to studying phase transitions. The consideration may be relevant to the study of the problem of existence of the spin glass phase in fermionic models.

hep-th↗
arXiv2018

A Note on the Eigenstate Thermalization Hypothesis

Eigenstate thermalization hypothesis (ETH) is discussed. We point out that the common formulation of the ETH suffers from the mixing of random and deterministic variables. We suggest a modified formulation of the ETH which includes only deterministic variables. We also show that this formulation of the ETH implies thermalization as well.

cond-mat.stat-mech↗
arXiv2018

Holographic control of information and dynamical topology change for composite open quantum systems

We investigate how the compositeness of a quantum system influences the characteristic time of equilibration. We study the dynamics of open composite quantum systems strongly coupled to the environment after a quantum perturbation accompanied by non-equilibrium heating. We use a holographic description of the evolution of entanglement entropy. The non-smooth character of the evolution with holographic entanglement is a general feature of composite systems, which demonstrate a dynamical change of topology in the bulk space and a jump-like velocity change of entanglement entropy propagation. Moreover, the number of jumps depends on the system configuration and especially on the number of composite parts. The evolution of the mutual information of two composite systems inherits these jumps. We present a detailed study of the mutual information for two subsystems with one of them being bipartite. We have found 5 qualitatively different types of behavior of the mutual information dynamics and indicated the corresponding ranges of system parameters.

hep-th↗
arXiv2018

Notes on the SYK model in real time

Nonperturbative formulation of the Sachdev-Ye-Kitaev (SYK) model is discussed. The partition function of the model can be represented as a functional integral over the Grassmann variables in Euclidean time which is well defined but it diverges after the transformation to the fermion bilocal fields. We point out that the generating functional of the SYK model in real time is well defined even after the transformation to the bilocal fields and it can be used for nonperturbative investigations of its properties. The SYK model in zero dimensions is studied, its large N expansion is evaluated and phase transitions are investigated.

hep-th↗
arXiv2016

Holographic Photosynthesis

There are successful applications of the holographic AdS/CFT correspondence to high energy and condensed matter physics. We apply the holographic approach to photosynthesis that is an important example of nontrivial quantum phenomena relevant for life which is being studied in the emerging field of quantum biology. Light harvesting complexes of photosynthetic organisms are many-body quantum systems, in which quantum coherence has recently been experimentally shown to survive for relatively long time scales even at the physiological temperature despite the decohering effects of their environments. We use the holographic approach to evaluate the time dependence of entanglement entropy and quantum mutual information in the Fenna-Matthews-Olson (FMO) protein-pigment complex in green sulfur bacteria during the transfer of an excitation from a chlorosome antenna to a reaction center. It is demonstrated that the time evolution of the mutual information simulating the Lindblad master equation in some cases can be obtained by means of a dual gravity describing black hole formation in the AdS-Vaidya spacetime. The wake up and scrambling times for various partitions of the FMO complex are discussed.

hep-th↗
arXiv2013

Photon flux and distance from the source: consequences for quantum foundations and technologies

The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) which limit the bit rate for long distances. Propagation of photons in optical fibers is modeled using methods of quantum electrodynamics. We define photon "duration" as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the linear dependence of photon duration on the distance. This effect puts the limit to joint increasing of the photon flux and the distance from the source and it has important consequences both for quantum information technologies and quantum foundations. Once quantum communication develops into a real technology, it would be appealing to the engineers to increase both the photon flux and the distance. And here our "photon flux/distance effect" has to be taken into account (at least if successively emitted photons are considered as independent). This effect also has to be taken into account in a loophole free test of Bell's type -- to close jointly the detection and locality loopholes.

quant-ph↗
arXiv2011

Bounds for the Distance Dependence of Correlation Functions of Entangled Photons in Waveguides

The distance dependence of the probability of observing two photons in a waveguide is investigated. The Glauber correlation functions of the entangled photons in waveguides are considered and the spatial and temporal dependence of the correlation functions is evaluated. We derive upper bounds to the distance dependence of the probability of observing two photons. These inequalities should be possible to observe in experiments.

quant-ph↗
arXiv2004

Generalized Quantum Turing Machine and its Application to the SAT Chaos Algorithm

Ohya and Volovich have proposed a new quantum computation model with chaotic amplification to solve the SAT problem, which went beyond usual quantum algorithm. In this paper, we generalize quantum Turing machine, and we show in this general quantum Turing machine (GQTM) that we can treat the Ohya-Volovich (OV) SAT algorithm.

quant-ph↗
arXiv2002

Local Realism, Contextualism and Loopholes in Bell`s Experiments

It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We show that such a claim can be justified only in a simplified approach to quantum mechanics when one neglects the fundamental fact that there exist space and time. Mathematical definitions of local realism in the sense of Bell and in the sense of Einstein are given. We demonstrate that if we include into the quantum mechanical formalism the space-time structure in the standard way then quantum mechanics might be consistent with Einstein's local realism. It shows that loopholes are unavoidable in experiments aimed to establish a violation of Bell`s inequalities. We show how the space-time structure can be considered from the contextual point of view. A mathematical framework for the contextual approach is outlined.

quant-ph↗
arXiv2002

Einstein, Podolsky and Rosen versus Bohm and Bell

There is an opinion that the Bohm reformulation of the EPR paradox in terms of spin variables is equivalent to the original one. In this note we show that such an opinion is not justified. We apply to the original EPR problem the method which was used by Bell for the Bohm reformulation. He has shown that correlation function of two spins cannot be represented by classical correlation of separated bounded random processes. This Bell`s theorem has been interpreted as incompatibility of local realism with quantum mechanics. We show that, in contrast to Bell`s theorem for spin or polarization correlation functions, the correlation of positions (or momenta) of two particles, depending on the rotation angles, in the original EPR model always admits a representation in the form of classical correlation of separated random processes. In this sense there exists a local realistic representation for the original EPR model but there is no such a representation for the Bohm spin reformulation of the EPR paradox. It shows also that the phenomena of quantum nonlocality is based not only on the properties of entangled states but also on the using of particular bounded observables.

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↗