Dynamical and statistical descriptions of N-body systems

Prigogine, I.; George, Claude; Henin, F.

doi:10.1016/0031-8914(69)90270-5

“…The operator P [a,b] has the following properties: 10) which are easily verified using the definition (B.8). Then, we see that operator U t is unitary, and satisfies…”

Section: A Itô and Stratonovich Calculusmentioning

confidence: 93%

Quantum stochastic differential equations for boson and fermion systems—method of non-equilibrium thermo field dynamics

Kobryn

¹

,

Hayashi

²

,

Arimitsu

³

2003

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…Of course, we could have obtained another solution by inverting the role of -ie and +ie but this second solution is of no physical relevance, 7 The iteration (5) leads to (11) and (12) with N 1 = 1. The normalization constant is defined afterwards.…”

Section: Complex Eigenvalue Problemmentioning

confidence: 99%

Quantum mechanics and the direction of time

Hasegawa

¹

,

Petrosky

²

,

Prigogine

³

et al. 1991

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…These arguments lead to the Boltzmann equation for dilute fluids, while for dense fluids they lead to the Fokker-Planek equation well known in the semimacroseopic theory of the Brownian motion. The averaging procedure over the phase can be described using projection operator techniques [5], the Nth order total phase distribution for the system being projected on to the sub-phase of one molecule or of a pair of molecules.…”

Section: Introductionmentioning

confidence: 99%

Systematic derivation of classical kinetic equations for simple dense fluids

Foster

¹

,

Cole

²

1971

Molecular Physics

3

0

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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Dynamical and statistical descriptions of N-body systems

Cited by 168 publications

References 6 publications

Quantum stochastic differential equations for boson and fermion systems—method of non-equilibrium thermo field dynamics

Quantum stochastic differential equations for boson and fermion systems—method of non-equilibrium thermo field dynamics

Quantum mechanics and the direction of time

Systematic derivation of classical kinetic equations for simple dense fluids

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