scholarly journals Simulation of three-dimensional quantum systems with projected entangled-pair states

2021 ◽  
Vol 103 (20) ◽  
Author(s):  
Patrick C. G. Vlaar ◽  
Philippe Corboz
Keyword(s):  
Three Dimensional ◽  
Quantum Systems

scholarly journals A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals

2020 ◽  
Vol 21 (11) ◽  
pp. 3499-3574
Author(s):  
Giovanni Antinucci ◽  
Luca Fresta ◽  
Marcello Porta
Keyword(s):  
Multiscale Analysis ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Supersymmetric Model ◽  
Energy Bands ◽  
Algebraic Decay ◽  
Group Methods ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Renormalization Group Methods

Abstract In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions.

WKB quantization rules for three-dimensional confinement

2001 ◽  
Vol 79 (6) ◽  
pp. 939-946 ◽  
Author(s):  
A Sinha ◽  
R Roychoudhury ◽  
Y P Varshni
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Reasonable Agreement ◽  
Three Dimensional ◽  
Quantum Systems ◽  
The Past ◽  
Two Systems ◽  
Mathematical Techniques ◽  
Confined Quantum Systems ◽  
Quantization Rules

Confined quantum systems have been studied by various authors over the past decades, by using various mathematical techniques. In this work, we derive the WKB quantization rules for quantum systems confined in an impenetrable spherical box of radius r0. We apply the proposed method to two systems explicitly, viz., the confined harmonic oscillator and the confined hydrogen atom. The results are found to be in reasonable agreement with those obtained by other methods. PACS No.: 03.65

scholarly journals A Generalised Linear Response Theory applied to the Dielectric Function of Coulomb Systems

2000 ◽  
Vol 53 (1) ◽  
pp. 133 ◽  
Author(s):  
H. Reinholz
Keyword(s):  
Dielectric Function ◽  
Linear Response ◽  
Electron Gas ◽  
Three Dimensional ◽  
Coulomb Systems ◽  
Linear Response Theory ◽  
Quantum Systems ◽  
Response Theory ◽  
Long Wavelength ◽  
Wave Numbers

A generalised linear response theory is used to derive the dielectric function at arbitrary wave numbers k and frequencies w for interacting quantum systems. The connection to thermodynamic Green functions allows the systematic perturbative treatment going beyond RPA and treating local field corrections as well as the inclusion of collisions on the same footing. Emphasis will be on the demonstration of the formalism. Results will be presented for the three-dimensional as well as two-dimensional case of an interacting electron gas. In the long-wavelength limit, a Drude-type expression with frequency dependent relaxation time is given bridging the theories of dielectric function and electrical conductivity.

HOW REAL ARE QUANTONS?

2004 ◽  
Vol 18 (04n05) ◽  
pp. 565-574
Author(s):  
MARCELLO CINI
Keyword(s):  
Quantum Mechanics ◽  
First Principles ◽  
Dimensional Space ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Wave Particle Duality ◽  
Wigner Representation ◽  
Large Quantum ◽  
Three Dimensional Space

In spite of the recent extraordinary progresses of experimental techniques it does not seem that, after more than seventy years from the birth of quantum mechanics, a unanimous consensus has been reached in the physicist's community on how to understand the "strange" properties of quantons, the wavelike/particlelike objects of the quantum world. In the first paragraph I will briefly recall some results on the problem of decoherence in large quantum systems, which at the same time may be viewed as an attempt of providing a "realistic" physical interpretation of the standard mathematical formulation of the theory. In the following ones I will present a derivation from first principles of the Wigner representation of quantum mechanics in phase space which eliminates altogether from the theory the Schrödinger waves and their questionable properties. This approach leads to the conclusion that the wave/particle duality has nothing to do with "probability waves", but is simply the manifestation of two complementary aspects (continuity vs. discontinuity) of an intrinsically nonlocal physical entity (the quantum field) which objectively exists in ordinary three dimensional space.

scholarly journals History and Some Aspects of the Lamb Shift

Physics ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 105-147 ◽  
Author(s):  
G. Jordan Maclay
Keyword(s):  
Energy Level ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Energy State ◽  
Energy Levels ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Zero Point ◽  
Quantum Systems ◽  
Vacuum Field

Radiation is a process common to classical and quantum systems with very different effects in each regime. In a quantum system, the interaction of a bound electron with its own radiation field leads to complex shifts in the energy levels of the electron, with the real part of the shift corresponding to a shift in the energy level and the imaginary part to the width of the energy level. The most celebrated radiative shift is the Lamb shift between the 2 s 1 / 2 and the 2 p 1 / 2 levels of the hydrogen atom. The measurement of this shift in 1947 by Willis Lamb Jr. proved that the prediction by Dirac theory that the energy levels were degenerate was incorrect. Hans Bethe’s calculation of the shift showed how to deal with the divergences plaguing the existing theories and led to the understanding that interactions with the zero-point vacuum field, the lowest energy state of the quantized electromagnetic field, have measurable effects, not just resetting the zero of energy. This understanding led to the development of modern quantum electrodynamics (QED). This historical pedagogic paper explores the history of Bethe’s calculation and its significance. It explores radiative effects in classical and quantum systems from different perspectives, with the emphasis on understanding the fundamental physical phenomena. Illustrations are drawn from systems with central forces, the H atom, and the three-dimensional harmonic oscillator. A first-order QED calculation of the complex radiative shift for a spinless electron is explored using the equations of motion and the m a s s 2 operator, describing the fundamental phenomena involved, and relating the results to Feynman diagrams.

scholarly journals MODELING DISORDERED QUANTUM SYSTEMS WITH DYNAMICAL NETWORKS

1999 ◽  
Vol 10 (04) ◽  
pp. 577-606 ◽  
Author(s):  
ROCHUS KLESSE ◽  
MARCUS METZLER
Keyword(s):  
Energy Levels ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Network Models ◽  
Quantum Systems ◽  
Electronic Systems ◽  
Dynamical Models ◽  
Static Properties ◽  
Three Dimensional Model ◽  
Metal Insulator

It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to quantum-dynamical models, which then allow for an investigation of dynamical and spectral aspects. This concept is exemplified by the Chalker–Coddington model for the quantum Hall effect and a three-dimensional generalization of it. We simulate phase coherent diffusion of wave packets and consider spatial and spectral correlations of network eigenstates as well as the distribution of (quasi-)energy levels. Apart from that, it is demonstrated how network models can be used to determine two-point conductances. Our numerical calculations for the three-dimensional model at the Metal-Insulator transition point delivers, among others, an anomalous diffusion exponent of η=3-D2=1.7±0.1. The methods presented here in detail have been used partially in earlier work.

scholarly journals Controlling the Shannon Entropy of Quantum Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yifan Xing ◽  
Jun Wu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Shannon Entropy ◽  
Quantum Control ◽  
Control Method ◽  
Controller Design ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Discretization Method

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

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