arXiv subjects

E. D. Vol

Publications and source records attributed to E. D. Vol.

At least 19 recordsLinked to original sources

arXiv2016

Small Entangled Quantum Worlds with a Simple Structure

We introduce the notion of a small quantum world (SQW) , which in our opinion, is very helpful in the situations when an experimenter's tools for preparing quantum states and (or) for measuring the observables of a quantum system under study are restricted due to some kind of reasons. In this case it is advisable to use as original an appropriate subspace of complete Hilbert space of states and respectively to utilize observables acting only in this subspace. If this subspace possesses some additional symmetries, the structure of a pure states set, as a rule, is simpler by far than in general case. Moreover in such SQWs some specific irreducible entangled states may appear. The similar states could be very helpful in various tasks connected with quantum informational applications. In the present paper main ideas outlined above are developed in detail in the simple and instructive case of a two-qubit system in which the accessible space of states possesses the additional symmetry structure of permutation group of three elements.

quant-ph↗

arXiv2015

The connection between phase synchronization in simple nonlinear system and stationary state entanglement in its quantum counterpart

We begin with the simple model of phase sychronization in open classical nonlinear system which is represented in the language of angular momentum variables. After that we propose the relevant quantum counterpart of this system. Using the appropriate Lindblad master equation for the density matrix of two qubit realization of such system we have revealed that stationary state of this composite system is pure and entangled with small dispersion of phase observable. We believe that such curious connection between entangled stationary states of quantum composite system and phase sychronization between its subsystems may be typical for rather wide class of similar nonlinear open systems as well.

quant-ph↗

arXiv2015

Quantum Look at two Common Logics: the Logic of Primitive Thinking and the Logic of Everyday Human Reasoning

Based on ideas of quantum theory of open systems and psychological dual system theory we propose two novel versions of Non-Boolean logic. The first version can be interpreted in our opinion as simplified description of primitive (mythological) thinking and the second one as the toy model of everyday human reasoning in which aside from logical deduction, heuristic elements and beliefs also play the considerable role. Several arguments in favor of the interpretations proposed are adduced and discussed in the paper as well.

q-bio.NC↗

arXiv2014

Quantum model of an autonomous oscillator in hard excitation regime

We propose the simple quantum model of nonlinear autonomous oscillator in hard excitation regime. We originate from classical equations of motion for similar oscillator and quantize them using the Lindblad master equation for the density matrix of this system. The solution for the populations of the stationary states of such oscillator may be explicitly found in the case when nonlinearity parameters of the problem are small. It was shown that in this situation there are three distinct regimes of behavior of the model. We compare properties of this model with corresponding ones of close open system, namely quantum oscillator in soft excitation regime. We discuss a possible applications of the results obtained.

quant-ph↗

arXiv2014

Quasithermodynamic Representation of the quantum master equations: its existence , advantages and applications

We propose a new representation for several quantum master equations in so-called quasithermodynamic form. This representation (when it exists) let one to write down dynamical equations both for diagonal and non-diagonal elements of density matrix of the quantum system of interest in unified form by means of nonequilibrium potential ("entropy") that is a certain quadratic function depending on all variables describing the state. We prove that above representation exists for the general Pauli master equation and for the Lindblad master equation ( at least in simple cases ) as well. We discuss also advantages of the representation proposed in the study of kinetic properties of open quantum systems particularly of its relaxation to the stationary state.

quant-ph↗

arXiv2014

Quasithermodynamic Representation of the Pauli Markov equation and their possible applications

We demonstrate that the extensive class of open Markov quantum systems describing by the Pauli master equation can be represented in so- called quasithermodynamic form .Such representation has certain advantages in many respects for example it allows one to specify precisely the parameter region in which the relaxation of the system in question to its stationary state occurs monotonically.With a view to illustrate possible applications of such representation we consider concrete Markov model that has in our opinion self-dependent interest namely the explanation of important and well established by numerous experiments the Yerkes-Dodson law in psychology

quant-ph↗

arXiv2013

The quantum approach to human reasoning does explain the belief-bias effect

Based on the ideas of quantum physics and dual-process theory of human reasoning that takes into account two primary mechanisms of reasoning : 1) deductive rational thinking and 2) intuitive heuristic judgment, we proposed the "quantum" approach to practical human logic that allows one to specify the most distinctive peculiarities in activity of two reasoning systems mentioned above and in addition to describe phenomenologically well-established experimentally belief-bias effect.

physics.soc-ph↗

arXiv2013

The Discrete-Continuous Logic and its possible quantum realizations

We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate that on the set of propositions of this kind one can define both the discrete logical operations (connectives) such as negation and strong logical disjunction and in addition one parameter group of continuous operations (logical rotations). We prove that an arbitrary classical proposition (which in this logic is represented by the purely diagonal matrix) can be considered as the result of strong disjunction of two identical GP. This fact gives one a good reason to presume the DCL as a prime logical substructure underlying to ordinary propositional logic, which is recorded by our consciousness. We believe that proposed version of DCL will find many applications both in physics (quantum logic) and also in cognitive sciences (mental imagery) for better understanding of the pecular nature of mental brain operations.

physics.soc-ph↗

arXiv2013

Quantum view on contextual logic of composite intelligent devices

Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units. In this preliminary communication we consider only the simplest example of such systems, namely, four- valued probabilistic logical device composed of two logical subsystems. We demonstrate that similar devices can generate two classes of probabilistic propositions:1) decomposable propositions, which in fact are equivalent to certain ordered pair of propositions in device subsystems and 2) indecomposable propositions which are connected with inherent logical interaction between device units. The indecomposable propositions are undoubtedly of greatest interest since they, as shown in the paper, provide powerful additional logical resource compared to standard parallel processing in composite intelligent systems. The contextual logic of composite devices proposed in this paper, as we believe, can be also used for analysis of highly organized systems in cognitive sciences specifically in neuropsychology and linguistics.

quant-ph↗

arXiv2012

Three "quantum" models of competition and cooperation in interacting biological populations and social groups

In present paper we propose the consistent statistical approach which appropriate for a number of models describing both behavior of biological populations and various social groups interacting with each other.The approach proposed based on the ideas of quantum theory of open systems (QTOS) and allows one to account explicitly both discreteness of a system variables and their fluctuations near mean values.Therefore this approach can be applied also for the description of small populations where standard dynamical methods are failed. We study in detail three typical models of interaction between populations and groups: 1) antagonistic struggle between two populations 2) cooperation (or, more precisely, obligatory mutualism) between two species 3) the formation of coalition between two feeble groups in their conflict with third one that is more powerful . The models considered in a sense are mutually complementary and include the most types of interaction between populations and groups. Besides this method can be generalized on the case of more complex models in statistical physics and also in ecology, sociology and other "soft' sciences.

physics.soc-ph↗

arXiv2012

Quantum theory as a relevant framework for the statement of probabilistic and many-valued logic

Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and examine it as density matrix of relevant quantum system. We are showing that all logical connectives between plausible propositions can be represented as special positive valued transformations of these matrices. We demonstrate also the above transformations can be realized in relevant composite quantum systems by quantum engineering methods. The approach proposed allows one not only to reproduce and generalize results of well-known logical systems (Boolean, Lukasiewicz and so on) but also to classify and analyze from unified point of view various actual problems in psychophysics and social sciences.

quant-ph↗

arXiv2012

Simple Quantum Model of Learning Explains the Yerkes-Dodson Law in Psychology

We propose the simple model of learning based on which we derive and explain the Yerkes-Dodson law - one of the oldest laws of experimental psychology. The approach uses some ideas of quantum theory of open systems (QTOS) and develops the method of statistical description of psychological systems that was proposed by author earlier.

physics.soc-ph↗

arXiv2011

Unified Statistical Description of Quasithermodynamic Systems in and out of Equilibrium

We propose the method of statistical description of broad class of dynamic systems (DS) whose equations of motion are determined by two state depending functions: 1) "energy" - the quantity which conserves in time and 2) "entropy" - the quantity which does not decrease in time. It is demonstrated that the behavior of such systems in the equilibrium state reduces to the thermodynamic lows in particular the Le Chatelier principle is satisfed and so on. Taking into account the interaction system of interest with ergometer - the device which continuously measures its energy one can possible to find the system distribution function in arbitrary non-equilibrium stationary state (NESS). Some general relations for mean values of certain quantities in NESS which can be compared with experimental data are obtained.

physics.class-ph↗

arXiv2011

Quantum theory as a tool for the description of simple psychological phenomena

We propose the consistent statistical approach for the quantitative description of simple psychological phenomena using the methods of quantum theory of open systems (QTOS). Taking as the starting point the K. Lewin's psychological field theory we show that basic concepts of this theory can be naturally represented in the language of QTOS. In particular provided that all stimuli acting on psychological system (that is individual or group of interest) are known one can associate with these stimuli corresponding operators and after that to write down the equation for evolution of density matrix of the relevant open system which allows one to find probabilities of all possible behavior alternatives. Using the method proposed we consider in detail simple model describing such interesting psychological phenomena as cognitive dissonance and the impact of competition among group members on its unity.

physics.soc-ph↗

arXiv2011

On the statistical description of classical open systems with integer variables by the Lindblad equation

We propose the consistent statistical approach to consider a wide class of classical open systems whose states are specified by a set of positive integers(occupation numbers).Such systems are often encountered in physics, chemistry, ecology, economics and other sciences.Our statistical method based on ideas of quantum theory of open systems takes into account both discreteness of the system variables and their time fluctuations - two effects which are ignored in usual mean field dynamical approach.The method let one to calculate the distribution function and (or)all moments of the system of interest at any instant.As descriptive examples illustrating the effectiveness of the method we consider some simple models:one relating to nonlinear mechanics,and others taken from population biology .In all this examples the results obtained by the method for large occupation numbers coincide with results of purely dynamical approach but for small numbers interesting differences and new effects arise.The possible observable effects connected with discreteness and fluctuations in such systems are discussed.

quant-ph↗

arXiv2010

On the relationship between quantum entanglement and classical synchronization in open systems

We propose a simple model of classical open system consisting of two subsystems all stationary states of which correspond to phase synchronization between the subsystems. The model is generalized to quantum systems in a finite-dimensional Hilbert space. The analysis of the simplest two qubit version of the quantum model shows that all its stationary states are nonseparable.

quant-ph↗

arXiv2007

The Characteristic Noise Induced by the Continious Measurements in Classical Open Systems

We proposed the modified version of quantum-mechanical theory of continuous measurements for the case of classical open systems. In our approach the influence of measurement on evolution of distribution function of an open system is described by the Fokker-Planck equation of a special form. The diffusion tensor of this equation is uniquely defined by a type of the measured quantity. On the basis of the approach proposed the stationary states of the linear dissipative systems, induced by measurements in them, are considered. Also we demonstrate on the simple example, how in the conservative system, consisting of noninteracting parts, measurement of the integral of motion results in relaxation to the quasi-thermodynamic equilibrium between parts of the system. The "temperature" of such state is determined by energy of the system and by the mean value of measured integral of motion. PACS numbers: 03.65.Ta, 05.40.-a

quant-ph↗

arXiv2005

Semiclassical quantization of non-Hamiltonian dynamical systems without memory

We propose a new method of quantization of a wide class of dynamical systems that originates directly from the equations of motion. The method is based on the correspondence between the classical and the quantum Poisson brackets, postulated by Dirac. This correspondence applied to open (non-Hamiltonian) systems allows one to point out the way of transition from the quantum description based on the Lindblad equation to the dynamical description of their classical analogs by the equations of motion and vice versa. As the examples of using of the method we describe the procedure of the quantization of three widely considered dynamical systems: 1) the harmonic oscillator with friction, 2) the oscillator with a nonlinear damping that simulates the process of the emergence of the limit cycle, and 3) the system of two periodic rotators with a weak interaction that synchronizes their oscillations. We discuss a possible application of the method for a description of quantum fluctuations in Josephson junctions with a strong damping and for the quantization of open magnetic systems with a dissipation and a pumping.

quant-ph↗