scholarly journals UNCERTAINTY RELATION FOR A QUANTUM OPEN SYSTEM

1995 ◽  
Vol 10 (31) ◽  
pp. 4537-4561 ◽  
Author(s):  
B.L. HU ◽  
YUHONG ZHANG
Keyword(s):  
Open System ◽  
Uncertainty Relation ◽  
Brownian Particle ◽  
Thermal Fluctuations ◽  
Generalized Uncertainty Relation ◽  
Decoherence Time ◽  
Statistical State ◽  
Classical Transition ◽  
Quantum Statistical ◽  
Quantum Open System

We derive the uncertainty relation for a quantum open system consisting of a Brownian particle interacting with a bath of quantum oscillators at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the system. We show that upon contact with the bath (assumed to be ohmic in this paper) the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time in similar models in the discussion of quantum to classical transition. This offers some insight into the physical mechanisms involved in the environment-induced decoherence process. We obtain closed analytic expressions for this generalized uncertainty relation under the conditions of high temperature and weak damping, separately. We also consider under these conditions an arbitrarily squeezed initial state and show how the squeeze parameter enters in the generalized uncertainty relation. Using these results we examine the transition of the system from a quantum pure state to a nonequilibrium quantum statistical state and to an equilibrium quantum statistical state. The three stages are marked by the decoherence time and the relaxation time, respectively. With these observations we explicate the physical conditions under which the two basic postulates of quantum statistical mechanics become valid. We also comment on the inappropriate usage of the word “classicality” in many decoherence studies of quantum to classical transition.

SQUEEZED STATES AND UNCERTAINTY RELATION AT FINITE TEMPERATURE

1993 ◽  
Vol 08 (37) ◽  
pp. 3575-3584 ◽  
Author(s):  
B.L. HU ◽  
YUHONG ZHANG
Keyword(s):  
Finite Temperature ◽  
Uncertainty Relation ◽  
Quantum Statistical Mechanics ◽  
Thermal Fluctuations ◽  
Squeezed States ◽  
Relative Importance ◽  
Initial State ◽  
Decoherence Time ◽  
Brownian Model ◽  
Quantum Open System

We use the quantum Brownian model to derive the uncertainty relation for a quantum open system in an arbitrarily-squeezed initial state interacting with an environment at finite temperature. We examine the relative importance of the quantum and thermal fluctuations in the evolution of the system towards equilibrium with the aim of clarifying the meaning of quantum, classical and thermal. We show that upon contact with the bath the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time calculated before in the context of quantum to classical transitions. We also use these results to deduce the conditions when the two basic postulates of quantum statistical mechanics become valid.

The generalized uncertainty relation and the quantum entropy of static spherical black hole surrounded by quintessence due to spin fields

2016 ◽  
Vol 94 (10) ◽  
pp. 1080-1084 ◽  
Author(s):  
Guqiang Li
Keyword(s):  
Black Hole ◽  
Uncertainty Relation ◽  
Brick Wall ◽  
Wall Model ◽  
Dominant Term ◽  
Gravitational Fields ◽  
Brick Wall Model ◽  
Generalized Uncertainty Relation ◽  
Spin Fields ◽  
Free Case

By using the brick-wall model, the quantum entropies of static spherical black hole surrounded by quintessence due to the Weyl neutrino, electromagnetic, massless Rarita–Schwinger, and gravitational fields for the source-free case are investigated from a generalized uncertainty relation. It is shown that in addition to the usual quadratically and logarithmically divergent terms, there exist additional quadratic, biquadratic, and logarithmic divergences at ultraviolet σ → 0, which not only depend on the black hole characteristics but also on the spins of the fields and the gravity correction factor. These additional terms describe the contribution of the quantum fields to the entropy and the effect of gravitational interactions on it. After the smallest length scale is taken into account, we find that the contribution of the gravitational interactions to the entropy is larger than the usual dominant term and becomes a part of the whole dominant term, so it is very important and cannot be neglected.

scholarly journals Thermal Fluctuations in Electric Circuits and the Brownian Motion

2010 ◽  
Vol 61 (4) ◽  
pp. 252-256 ◽  
Author(s):  
Gabriela Vasziová ◽  
Jana Tóthová ◽  
Lukáš Glod ◽  
Vladimír Lisý
Keyword(s):  
Brownian Motion ◽  
Brownian Particle ◽  
Mean Square Displacement ◽  
Thermal Fluctuations ◽  
Stochastic Equations ◽  
Thermal Bath ◽  
Current Fluctuations ◽  
Electric Circuits ◽  
The Mean ◽  
Optically Trapped

Thermal Fluctuations in Electric Circuits and the Brownian MotionIn this work we explore the mathematical correspondence between the Langevin equation that describes the motion of a Brownian particle (BP) and the equations for the time evolution of the charge in electric circuits, which are in contact with the thermal bath. The mean quadrate of the fluctuating electric charge in simple circuits and the mean square displacement of the optically trapped BP are governed by the same equations. We solve these equations using an efficient approach that allows us converting the stochastic equations to ordinary differential equations. From the obtained solutions the autocorrelation function of the current and the spectral density of the current fluctuations are found. As distinct from previous works, the inertial and memory effects are taken into account.

Generalized Wigner–Yanase–Dyson information revisited

2016 ◽  
Vol 19 (03) ◽  
pp. 1650022
Author(s):  
Liang Cai
Keyword(s):  
Fisher Information ◽  
Uncertainty Relation ◽  
Direct Approach ◽  
Fundamental Properties ◽  
Generalized Uncertainty Relation

Motivated by the direct approach to quantum extensions of Fisher information in Chen and Luo [Front. Math. China 2 (2007) 359], we introduce a further generalized version of Wigner–Yanase–Dyson information, and investigate its fundamental properties including positivity, convexity and super-additivity, etc. As an application, we present a generalized uncertainty relation.

EFFECT OF THE GENERALIZED UNCERTAINTY RELATION ON THE BLACK HOLE ENTROPY

2002 ◽  
Vol 17 (33) ◽  
pp. 2209-2219
Author(s):  
XIANG LI
Keyword(s):  
Black Hole ◽  
Uncertainty Relation ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
Wall Model ◽  
Dirac Fields ◽  
Brick Wall Model ◽  
Generalized Uncertainty Relation ◽  
Klein Gordon ◽  
The Difference

The quantum entropies of the black hole, due to the massless Klein–Gordon and Dirac fields, are investigated by Rindler approximation. The difference from the brick wall model is that we take into account the effect of the generalized uncertainty relation on the state counting. The divergence appearing in the brick wall model is removed and the entropies proportional to the horizon area come from the contributions of the modes in the vicinity of the horizon. Here we take the units G=c=ℏ=kB=1.

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.

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