scholarly journals Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics

2021 ◽  
Author(s):  
Ladislaus Alexander Bányai ◽  
Mircea Bundaru ◽  
Paul Gartner
Keyword(s):  
Wave Vector ◽  
Quantum Statistical Mechanics ◽  
Field Operator ◽  
Thermal Fluctuations ◽  
Noise Spectrum ◽  
Complex Frequency ◽  
Occupation Numbers ◽  
Interacting Electrons ◽  
Quantum Statistical ◽  
The Fourier Transform

We derive the thermal noise spectrum of the Fourier transform of the electric field operator of a given wave vector starting from the quantum-statistical definitions and relate it to the complex frequency and wave vector dependent complex conductivity in a homogeneous, isotropic system of electromagnetic interacting electrons. We analyze separately the longitudinal and transverse case with their peculiarities. The Nyquist formula for vanishing frequency and wave vector, as well as its modification for non-vanishing frequencies and wave vectors follow immediately. Furthermore we discuss also the noise of the photon occupation numbers. It is important to stress that no additional assumptions at all were used in this straightforward proof.

scholarly journals Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics

2021 ◽  
Author(s):  
Ladislaus Alexander Bányai ◽  
Mircea Bundaru ◽  
Paul Gartner
Keyword(s):  
Wave Vector ◽  
Quantum Statistical Mechanics ◽  
Field Operator ◽  
Thermal Fluctuations ◽  
Noise Spectrum ◽  
Complex Frequency ◽  
Occupation Numbers ◽  
Interacting Electrons ◽  
Quantum Statistical ◽  
The Fourier Transform

We derive the thermal noise spectrum of the Fourier transform of the electric field operator of a given wave vector starting from the quantum-statistical definitions and relate it to the complex frequency and wave vector dependent complex conductivity in a homogeneous, isotropic system of electromagnetic interacting electrons. We analyze separately the longitudinal and transverse case with their peculiarities. The Nyquist formula for vanishing frequency and wave vector, as well as its modification for non-vanishing frequencies and wave vectors follow immediately. Furthermore we discuss also the noise of the photon occupation numbers. It is important to stress that no additional assumptions at all were used in this straightforward proof.

scholarly journals Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics.

2022 ◽  
Author(s):  
Ladislaus Bányai
Keyword(s):  
Wave Vector ◽  
Transverse Electric ◽  
Quantum Statistical Mechanics ◽  
Field Operator ◽  
Thermal Fluctuations ◽  
Noise Spectrum ◽  
Complex Frequency ◽  
Occupation Numbers ◽  
Interacting Electrons ◽  
Quantum Statistical

We derive the thermal noise spectrum of the of the longitudinal and transverse electric field operator of a given wave vector starting from the quantum-statistical definitions and relate it to the complex frequency and wave vector dependent complex conductivity in a homogeneous, isotropic system of electromagnetic interacting electrons. No additional assumptions were used in the proof. We analyze separately the longitudinal and transverse case with their peculiarities. The Nyquist formula for vanishing frequency and wave vector, as well as its modification for non-vanishing frequencies and wave vectors follow immediately. Furthermore we discuss also the noise of the photon occupation numbers.

scholarly journals Reality of the Wigner Functions and Quantization

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Sadollah Nasiri ◽  
Samira Bahrami
Keyword(s):  
Phase Space ◽  
Quantum Statistical Mechanics ◽  
Direct Consequence ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Reality Condition ◽  
Energy Quantization ◽  
Extended Action ◽  
Space Formulation ◽  
Quantum Statistical

Here we use the extended phase space formulation of quantum statistical mechanics proposed in an earlier work to define an extended lagrangian for Wigner's functions (WFs). The extended action defined by this lagrangian is a function of ordinary phase space variables. The reality condition of WFs is employed to quantize the extended action. The energy quantization is obtained as a direct consequence of the quantized action. The technique is applied to find the energy states of harmonic oscillator, particle in the box, and hydrogen atom as the illustrative examples.

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