Fluctuation removal around spectral and temporal constancy limits via use of an extended space expectation value weight function for singular quantum systems

2015 ◽  
Author(s):  
Berfin Kalay ◽  
Metin Demiralp
Keyword(s):  
Weight Function ◽  
Quantum Systems ◽  
Expectation Value ◽  
Extended Space

scholarly journals A Proof of the Bloch Theorem for Lattice Models

2019 ◽  
Vol 177 (4) ◽  
pp. 717-726 ◽  
Author(s):  
Haruki Watanabe
Keyword(s):  
Boundary Condition ◽  
Tight Binding ◽  
Lattice Models ◽  
Quantum Systems ◽  
Open Boundary ◽  
Current Operator ◽  
Open Boundary Condition ◽  
Expectation Value ◽  
Bloch Theorem ◽  
Large Quantum

Abstract The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibrium at a finite temperature, irrespective of the details of the Hamiltonian as far as all terms in the Hamiltonian are finite ranged. In this work we present a simple yet rigorous proof for general lattice models. For large but finite systems, we find that both the discussion and the conclusion are sensitive to the boundary condition one assumes: under the periodic boundary condition, one can only prove that the current expectation value is inversely proportional to the linear dimension of the system, while the current expectation value completely vanishes before taking the thermodynamic limit when the open boundary condition is imposed. We also provide simple tight-binding models that clarify the limitation of the theorem in dimensions higher than one.

Quantum phase transitions without thermodynamic limits

2007 ◽  
Vol 463 (2084) ◽  
pp. 2021-2030 ◽  
Author(s):  
Dorje C Brody ◽  
Daniel W Hook ◽  
Lane P Hughston
Keyword(s):  
Phase Transitions ◽  
Equilibrium State ◽  
Density Of States ◽  
Quantum Phase Transitions ◽  
Quantum Systems ◽  
State Spaces ◽  
Expectation Value ◽  
Finite Dimensional ◽  
Finite Quantum Systems ◽  
Thermodynamic Limits

A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterized by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function. It is demonstrated that generic quantum systems therefore exhibit second-order phase transitions at finite temperatures.

scholarly journals Macroscopic Limit of Quantum Systems

Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 315
Author(s):  
Janos Polonyi
Keyword(s):  
Quantum Systems ◽  
Classical Trajectory ◽  
Time Dependent ◽  
Large Set ◽  
Measuring Apparatus ◽  
Technical Device ◽  
Expectation Value ◽  
Avogadro’S Number ◽  
The Central Limit Theorem ◽  
Quantum Version

Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro’s number. This result refers to the observed system without considering the measuring apparatus. The emergence of a classical trajectory is followed qualitatively in Wilson’s cloud chamber.

scholarly journals Quantum confinement in 1D systems through an imaginary-time evolution method

2015 ◽  
Vol 30 (37) ◽  
pp. 1550176 ◽  
Author(s):  
Amlan K. Roy
Keyword(s):  
Time Evolution ◽  
Excited States ◽  
Quantum Confinement ◽  
Global Minimum ◽  
Quantum Systems ◽  
Attractive Potential ◽  
Imaginary Time ◽  
Expectation Values ◽  
Expectation Value ◽  
Orthogonality Constraint

Quantum confinement is studied by numerically solving time-dependent (TD) Schrödinger equation (SE). An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum. Excited states are obtained by imposing the orthogonality constraint with all lower states. Applications are made on three important model quantum systems, namely, harmonic, repulsive and quartic oscillators; enclosed inside an impenetrable box. The resulting diffusion equation is solved using finite-difference method. Both symmetric and asymmetric confinement are considered for attractive potential; for others only symmetrical confinement. Accurate eigenvalue, eigenfunction and position expectation values are obtained, which show excellent agreement with existing literature results. Variation of energies with respect to box length is followed for small, intermediate and large sizes. In essence, a simple accurate and reliable method is proposed for confinement in quantum systems.

scholarly journals Modeling the Impact of Hamiltonian Perturbations on Expectation Value Dynamics

2020 ◽  
Vol 75 (5) ◽  
pp. 475-481
Author(s):  
Robin Heveling ◽  
Lars Knipschild ◽  
Jochen Gemmer
Keyword(s):  
Spin System ◽  
Numerical Experiments ◽  
Numerical Data ◽  
Quantum Systems ◽  
Relaxation Dynamics ◽  
Expectation Value ◽  
Weak Perturbation ◽  
Expectation Value Dynamics ◽  
The Impact

AbstractEvidently, some relaxation dynamics, e.g. exponential decays, are much more common in nature than others. Recently there have been attempts to explain this observation on the basis of “typicality of perturbations” with respect to their impact on expectation value dynamics. These theories suggest that a majority of the very numerous, possible Hamiltonian perturbations entail more or less the same type of alteration of the decay dynamics. Thus, in this paper, we study how the approach towards equilibrium in closed quantum systems is altered due to weak perturbations. To this end, we perform numerical experiments on a particular, exemplary spin system. We compare our numerical data to predictions from three particular theories. We find satisfying agreement in the weak perturbation regime for one of these approaches.

Correlation analysis of radiation damage

1978 ◽  
Vol 36 (1) ◽  
pp. 214-215
Author(s):  
R. Hegerl ◽  
A. Feltynowski ◽  
B. Grill
Keyword(s):  
Electron Microscopy ◽  
Independent Random Variables ◽  
Optical Parameters ◽  
Bright Field Image ◽  
Bright Field ◽  
Expectation Value ◽  
All Optical ◽  
Image Element ◽  
Stochastic Series ◽  
The Common

Till now correlation functions have been used in electron microscopy for two purposes: a) to find the common origin of two micrographs representing the same object, b) to check the optical parameters e. g. the focus. There is a third possibility of application, if all optical parameters are constant during a series of exposures. In this case all differences between the micrographs can only be caused by different noise distributions and by modifications of the object induced by radiation.Because of the electron noise, a discrete bright field image can be considered as a stochastic series Pm,where i denotes the number of the image and m (m = 1,.., M) the image element. Assuming a stable object, the expectation value of Pm would be Ηm for all images. The electron noise can be introduced by addition of stationary, mutual independent random variables nm with zero expectation and the variance. It is possible to treat the modifications of the object as a noise, too.

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