A New Approach to Quantum-Statistical Mechanics

Matsubara, Takeo

doi:10.1143/ptp.14.351

Cited by 1,202 publications

(737 citation statements)

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“…Finite-temperature many-body perturbation theory (FT-MBPT) [14,15,17,18,19] is based on the grand-canonical ensemble [27]. The fundamental quantity describing the state of a system in the grand-canonical ensemble, such that the parameters of the theory are the temperature T (or β = 1/T in suitable units), the volume V , and the chemical potential µ, is the density operator…”

Section: Finite-temperature Many-body Perturbation Theorymentioning

confidence: 99%

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Finite-temperature second-order many-body perturbation theory revisited

Santra

Schirmer

2017

Chemical Physics

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We present an algebraic, nondiagrammatic derivation of finite-temperature second-order many-body perturbation theory [FT-MBPT(2)], using techniques and concepts accessible to theoretical chemical physicists. We give explicit expressions not just for the grand potential but particularly for the mean energy of an interacting many-electron system. The framework presented is suitable for computing the energy of a finite or infinite system in contact with a heat and particle bath at finite temperature and chemical potential. FT-MBPT(2) may be applied if the system, at zero temperature, may be described using standard (i.e., zero-temperature) second-order many-body perturbation theory [ZT-MBPT(2)] for the energy. We point out that in such a situation, FT-MBPT(2) reproduces, in the zero-temperature limit, the energy computed within ZT-MBPT(2). In other words, the difficulty that has been referred to as the Kohn-Luttinger conundrum, does not occur. We comment, in this context, on a "renormalization" scheme recently proposed by Hirata and He.

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Section: Finite-temperature Many-body Perturbation Theorymentioning

confidence: 99%

“…(11). To this end, note that the operatorÛ (β) = e −β(Ĥ−µN ) (17) appearing in Eq. (11) has the structure of a time evolution operator with time argument −iβ ("imaginary time") and HamiltonianĤ − µN .…”

Section: Finite-temperature Many-body Perturbation Theorymentioning

confidence: 99%

Finite-temperature second-order many-body perturbation theory revisited

Santra

Schirmer

2017

Chemical Physics

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“…In the imaginary-time formalism of the thermal field theory [9], the Matsubara propagator is defined by…”

Section: B Thermal Field Theorymentioning

confidence: 99%

Momentum dependence of the spectral functions in theO(4)linear sigma model at finite temperature

2003

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The spatial momentum dependence of the spectral function for π and σ at finite temperature is studied by employing the O(4) linear sigma model and adopting a resummation technique called optimized perturbation theory (OPT). The poles of the propagators are also searched for.We analyze the spatial momentum dependence of the imaginary part of the self-energy and find its temperature-dependent part to vanish in the large momentum limit. This is because the energy of the particles in the heat bath which participate in the process becomes large and therefore the Bose distribution function vanishes.We then calculate the spectral functions and search for the poles of the propagators. First, we discuss the temperature dependence for zero spatial momentum. We reproduce the spectral functions in both π and σ channels in the previous work and find that the pole, which is responsible for the threshold enhancement of the spectral functions in both π and σ channels, is different from the one for the peak at zero temperature. Secondly, we discuss the spatial-momentum dependence.When the temperature is low the spatial momentum dependence is also small. As the temperature becomes higher the spatial momentum dependence becomes also large. When the spatial momentum is smaller than the temperature, the spectral functions do not deviate much from those at zero spatial momentum. Once the spatial momentum becomes comparable with the temperature, the deviation becomes considerable. As the momentum becomes much larger than the temperature, thermal effects effectively decrease.

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“…This resummation procedure, however, generates appreciable magnitude of the imaginary part to the self energy at the same time, so that the delta function seen in (19) will no longer be present as we see below. Thus we expect that the use of a resummed propagator changes the result qualitatively, and that the simple observation that a large thermal mass would close the phase space of the decay rate of the inflaton (18) would not apply.…”

Section: Inclusion Of the Thermal Mass Of The Decay Productsmentioning

confidence: 99%

“…The effect of the thermal environment on χ, which gives rise to finite-temperature correction to its mass, can be incorporated to the calculation of the dissipation rate of φ if we apply resummation and use a resummed propagator of χ instead of the finite-temperature bare Feynman propagator (8) to calculate the effective action. With the help of the Matsubara formalism [18], the denominator of the propagator acquires a self energy whose real part yields a finite-temperature correction to the mass as desired. This resummation procedure, however, generates appreciable magnitude of the imaginary part to the self energy at the same time, so that the delta function seen in (19) will no longer be present as we see below.…”

Section: Inclusion Of the Thermal Mass Of The Decay Productsmentioning

confidence: 99%

Can oscillating scalar fields decay into particles with a large thermal mass?

Yokoyama

2006

Physics Letters B

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We calculate the dissipation rate of a coherently oscillating scalar field in a thermal environment using nonequilibrium quantum field theory and apply it to the reheating stage after cosmic inflation. It is shown that the rate is nonvanishing even when particles coupled to the oscillating inflaton field have a larger thermal mass than it, and therefore the cosmic temperature can be much higher than inflaton's mass even in the absence of preheating. Its cosmological implications are also discussed.

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A New Approach to Quantum-Statistical Mechanics

Cited by 1,202 publications

References 0 publications

Finite-temperature second-order many-body perturbation theory revisited

Finite-temperature second-order many-body perturbation theory revisited

Momentum dependence of the spectral functions in theO(4)linear sigma model at finite temperature

Can oscillating scalar fields decay into particles with a large thermal mass?

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