Statistical Theory of Open Systems

Klimontovich, Yu. L.

doi:10.1007/978-94-011-0175-2

Cited by 315 publications

(259 citation statements)

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“…The decay of the transverse polarization, perpendicular to the permanently applied field, is in general characterized by the relaxation time T 2 ; it can be viewed as a decoherence of the spin system, since it exhibits the decay of the off-diagonal contributions to the spin density matrix in the representation where the applied Hamiltonian is diagonal [204,205]. Another standard example is related to the Pauli equation for an open quantum system weakly coupled to an external thermal bath [206]. This equation can be visualized as a classical stochastic process during which the system transits from one energy level to another.…”

Section: Decoherence Theorymentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Decoherence Theorymentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…(Lorenz, 1993) Ende der 60er greift Prigogine mit Glansdorff und Nicolis erneut das Problem der Prozesse weitab vom thermodynamischen Gleichgewicht auf und analysiert die vorliegenden Experimente, wie die Belousov-Zabotinsky-Reaktion. Im Resultat entstehen die Grundlagen der modernen Theorie der Selbstorganisation (Glansdorff & Prigogine, 1971;Nicolis & Prigogine, 1977 (Klimontovich, 1995). (Ebeling und Feistel, 1982, Festel und Ebeling, 2011 (Maturana, Varela, 1987 (Schweitzer, 1997;Helbing, 1997, Galam, 2012 Ebeling, Engel & Feistel, 1990 Weidlich, Haag, 1983;Saam 1995).…”

Section: Abbildung 2: Wachstum Der Dokumente Zur Selbstorganisation Iunclassified

Handbuch Modellbildung und Simulation in den Sozialwissenschaften

Braun¹,

Saam²

2015

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“…In fact, by following the traditional pattern of hydrodynamical formalism, [14,16], we infer the closed system of two (which is special to Markovian diffusions !) local conservation laws for the Smoluchowski process, [11,13]:…”

Section: Hydrodynamical Formalism For Random Dynamicsmentioning

confidence: 99%

“…We are interested in passing to a hydrodynamical picture, following the traditional recipes [14,16]. To that end we need to propagate certain initial probability density and investigate effects of the random dynamics.…”

Section: Kramers Equation and Local Conservation Lawsmentioning

confidence: 99%

“…Let us mention that, as reveals the hydrodynamical formalism of the Brownian motion, [14], Brownian particles "while being thermalized", show up a continual net absorption of heat/energy from the reservoir (that point is normally disregarded in view of the very short relaxation times): socalled kinetic temperature grows up to the actual temperature of the bath, in parallel with the mean kinetic energy of the Brownian particle, [11,15,6], c.f. also [16,17].…”

Section: Introductionmentioning

confidence: 99%

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Frictionless random dynamics: hydrodynamical formalism

Czopnik

Garbaczewski

2003

Physica A: Statistical Mechanics and its Applications

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We investigate an undamped random phase-space dynamics in deterministic external force fields (conservative and magnetic ones). By employing the hydrodynamical formalism for those stochastic processes we analyze microscopic kinetic-type "collision invariants" and their relationship to local conservation laws (moment equations) in the fully nonequlibrium context. We address an issue of the continual heat absorption (particles "energization") in the course of the process and its possible physical implementations. IntroductionThe major topic discussed in the present paper will be the frictionless random motion which is introduced in close affinity with second-order processes driven by white noise, [1,2]. In the course of motion an unrestricted "energization" of particles is possible, a phenomenon which has not received much attention in the literature, although appears to be set on convincing phenomenological grounds in specific (nontypical) physical surroundings, [3,4].A classic problem of an irreversible behaviour of a particle embedded in the large encompassing system, [5,6,7] pertains to the random evolution of tracer particles in a fluid (like e.g. those performing Brownian motion). In that case, a particle -bath coupling is expected to imply quick relaxation towards a stationary probability distribution (equilibrium Maxwellian for a given a priori temperature T of the surrounding fluid/bath) and thus making the system amenable to standard fluctuationdissipation theorems. The dissipation of randomly acquired energy back to the bath is here enforced by dynamical friction mechanisms, [8,9,10,7], although no balance between stochastic forcing (random *

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Statistical Theory of Open Systems

Cited by 315 publications

References 0 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Handbuch Modellbildung und Simulation in den Sozialwissenschaften

Frictionless random dynamics: hydrodynamical formalism

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