scholarly journals Initial states for quantum field simulations in phase space

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Peter D. Drummond ◽  
Bogdan Opanchuk
Keyword(s):  
Phase Space ◽  
Quantum Field ◽  
Initial States

scholarly journals Coherent representation of fields and deformation quantization

2020 ◽  
Vol 17 (11) ◽  
pp. 2050166 ◽  
Author(s):  
Jasel Berra-Montiel ◽  
Alberto Molgado
Keyword(s):  
Phase Space ◽  
Deformation Quantization ◽  
Probability Distributions ◽  
Series Representation ◽  
Quantum Field ◽  
Husimi Distribution ◽  
Normal Star ◽  
Holomorphic Representation ◽  
Functional Distribution ◽  
Space Description

Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows to establish a [Formula: see text]-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution, which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.

scholarly journals Fidelity of Gaussian Channels

2004 ◽  
Vol 11 (04) ◽  
pp. 309-323 ◽  
Author(s):  
Carlton M. Caves ◽  
Krzysztof Wódkiewicz
Keyword(s):  
Phase Space ◽  
Scaling Law ◽  
Continuous Variable ◽  
Gaussian Channel ◽  
Quantum Cloning ◽  
Field Mode ◽  
Universal Scaling ◽  
Input Field ◽  
Gaussian Channels ◽  
Initial States

A noisy Gaussian channel is defined as a channel in which an input field mode is subjected to random Gaussian displacements in phase space. We introduce the quantum fidelity of a Gaussian channel for pure and mixed input states, and we derive a universal scaling law of the fidelity for pure initial states. We also find the maximum fidelity of a Gaussian channel over all input states. Quantum cloning and continuous-variable teleportation are presented as physical examples of Gaussian channels to which the fidelity results can be applied.

scholarly journals Statistics of the Bifurcation in Quantum Measurement

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 834 ◽  
Author(s):  
Karl-Erik Eriksson ◽  
Kristian Lindgren
Keyword(s):  
Field Theory ◽  
Quantum Measurement ◽  
Measurement Process ◽  
Quantum Field ◽  
Born Rule ◽  
Level System ◽  
Measurement Device ◽  
Final State ◽  
Initial States ◽  
Quantum Measurement Process

We model quantum measurement of a two-level system μ . Previous obstacles for understanding the measurement process are removed by basing the analysis of the interaction between μ and the measurement device on quantum field theory. This formulation shows how inverse processes take part in the interaction and introduce a non-linearity, necessary for the bifurcation of quantum measurement. A statistical analysis of the ensemble of initial states of the measurement device shows how microscopic details can influence the transition to a final state. We find that initial states that are efficient in leading to a transition to a final state result in either of the expected eigenstates for μ , with ensemble averages that are identical to the probabilities of the Born rule. Thus, the proposed scheme serves as a candidate mechanism for the quantum measurement process.

scholarly journals PHASE SPACE PROPERTIES OF CHARGED FIELDS IN THEORIES OF LOCAL OBSERVABLES

1995 ◽  
Vol 07 (04) ◽  
pp. 527-557 ◽  
Author(s):  
D. BUCHHOLZ ◽  
C. D’ANTONI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Space ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Space Analysis ◽  
Algebraic Quantum ◽  
Thermal Features ◽  
Local Observables

Within the setting of algebraic quantum field theory a relation between phase-space properties of observables and charged fields is established. These properties are expressed in terms of compactness and nuclearity conditions which are the basis for the characterization of theories with physically reasonable causal and thermal features. Relevant concepts and results of phase space analysis in algebraic quantum field theory are reviewed and the underlying ideas are outlined.

Quantum field theory in phase space

2019 ◽  
Vol 34 (08) ◽  
pp. 1950037 ◽  
Author(s):  
R. G. G. Amorim ◽  
F. C. Khanna ◽  
A. P. C. Malbouisson ◽  
J. M. C. Malbouisson ◽  
A. E. Santana
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Phase Space ◽  
Relativistic Quantum ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Klein Gordon ◽  
Quantization Rules

The tilde conjugation rule in thermofield dynamics, equivalent to the modular conjugation in a [Formula: see text]-algebra, is used to develop unitary representations of the Poincaré group, where the Hilbert space has the phase space content, a symplectic Hilbert space. The state is described by a quasi-amplitude of probability, which is a sort of wave function in phase space, associated with the Wigner function. The quantum field theory in phase space is then constructed, including the quantization rules for the Klein–Gordon and the Dirac fields, the derivation of the electrodynamics in phase space and elements of a relativistic quantum kinetic theory. Towards a physical interpretation of the theory, propagators are associated with the corresponding Wigner functions. The Feynman rules follow accordingly with vertices similar to those of usual non-Abelian quantum field theories.

scholarly journals Structural Criticality of Dynamical Glass State in a Spatially Extended Dynamical System

1997 ◽  
Vol 07 (05) ◽  
pp. 1043-1052
Author(s):  
Hiroki Hata ◽  
Kimitoshi Yabe
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Control Parameters ◽  
Finite Region ◽  
Initial State ◽  
Glass State ◽  
Periodic Attractors ◽  
Spatially Extended ◽  
Initial States ◽  
Almost All

Many periodic attractors frequently coexist in the phase space of a spatially extended dynamical system, and such a state is called the dynamical glass state [Fujisaka et al., 1993]. We study numerically the dynamical glass state of a coupled map system and find that the measure of the structurally critical attractors (just before the bifurcation points) is large. Hence, the global basin structure of the dynamical glass state is "critical". And the dynamical glass state is observed in a finite region in the parameter space, therefore almost all the trajectories made from random initial states focus on the structurally critical attractors without tuning any control parameters in the region. This interesting new property and the relaxation process from an initial state to one of the final attractors are reported.

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