233 research outputs found
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.-aComment: 13 p., 0 fi
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.Comment: 6 page
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.Comment: 6 pages, no figure
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 psychologyComment: 5 page
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.Comment: 7 page
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.Comment: 4 page
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.Comment: 11 page
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.Comment: 8 pages, 0 figure
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.Comment: 7 page
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
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