scholarly journals Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1544
Author(s):  
Jen-Tsung Hsiang ◽  
Bei-Lok Hu
Keyword(s):  
Quantum Dynamics ◽  
Coarse Graining ◽  
Von Neumann Entropy ◽  
Quantum Field ◽  
Matrix Elements ◽  
Cosmological Perturbations ◽  
Von Neumann ◽  
Particle Pairs ◽  
Field Fluctuations ◽  
The Universe

Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field.

scholarly journals Quantum reversibility is relative, or does a quantum measurement reset initial conditions?

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170315 ◽  
Author(s):  
Wojciech H. Zurek
Keyword(s):  
Quantum Dynamics ◽  
Quantum Physics ◽  
Information Gain ◽  
Initial Conditions ◽  
Foundations Of Quantum Mechanics ◽  
Von Neumann Entropy ◽  
Quantum Evolution ◽  
Von Neumann ◽  
The Universe

I compare the role of the information in classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer’s retention of the information about the measurement outcome. By contrast—even though quantum dynamics is unitary, hence, reversible—reversing quantum evolution that led to a measurement becomes, in principle, impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss—rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer’s (branch of) the Universe. Nevertheless, I also show that the observer’s friend—an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result—can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

scholarly journals MONOTONICITY OF QUANTUM RELATIVE ENTROPY REVISITED

2003 ◽  
Vol 15 (01) ◽  
pp. 79-91 ◽  
Author(s):  
DÉNES PETZ
Keyword(s):  
Relative Entropy ◽  
Coarse Graining ◽  
Von Neumann Entropy ◽  
Trace Inequality ◽  
Von Neumann ◽  
Quantum Relative Entropy ◽  
Crucial Property

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden–Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly indicated.

scholarly journals Quantum thermodynamics and quantum entanglement entropies in an expanding universe

2017 ◽  
Vol 32 (15) ◽  
pp. 1750066 ◽  
Author(s):  
Mehrnoosh Farahmand ◽  
Hosein Mohammadzadeh ◽  
Hossein Mehri-Dehnavi
Keyword(s):  
Scalar Field ◽  
Quantum Entanglement ◽  
Particle Creation ◽  
Space Time ◽  
Von Neumann Entropy ◽  
Quantum Thermodynamics ◽  
Entanglement Generation ◽  
Von Neumann ◽  
Underlying Space ◽  
The Universe

We investigate an asymptotically spatially flat Robertson–Walker space–time from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in space–time. Then, we work out the entropy of particle creation based on the quantum thermodynamics of the scalar field on the underlying space–time. We show that the general behavior of both entropies are the same. Therefore, the entanglement can be applied to the customary quantum thermodynamics of the universe. Also, using these entropies, we can recover some information about the parameters of space–time.

scholarly journals Quantum Features of Macroscopic Fields: Entropy and Dynamics

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 705
Author(s):  
Robert Alicki
Keyword(s):  
Wave Equations ◽  
Particle Density ◽  
Von Neumann Entropy ◽  
Quantum Field ◽  
Von Neumann ◽  
Single Particle Density ◽  
Definition Of ◽  
Thermal Sources ◽  
Reduced State ◽  
State Of The Field

Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of the field combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equation for the reduced state of the field is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of entropy for the reduced state of the field follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows unifying the Mueller and Jones calculi in polarization optics.

scholarly journals Large deviation bounds for k -designs

2009 ◽  
Vol 465 (2111) ◽  
pp. 3289-3308 ◽  
Author(s):  
Richard A. Low
Keyword(s):  
Haar Measure ◽  
Random Distribution ◽  
Large Deviation ◽  
Von Neumann Entropy ◽  
General Technique ◽  
Von Neumann ◽  
Canonical State ◽  
Random States ◽  
The Universe ◽  
Random State

We present a technique for de-randomizing large deviation bounds of functions on the unitary group. We replace the Haar measure with a pseudo-random distribution, a k -design. k -Designs have the first k moments equal to those of the Haar measure. The advantage of this is that (approximate) k -designs can be implemented efficiently, whereas Haar random unitaries cannot. We find large deviation bounds for unitaries chosen from a k -design and then illustrate this general technique with three applications. We first show that the von Neumann entropy of a pseudo-random state is almost maximal. Then we show that, if the dynamics of the universe produces a k -design, then suitably sized subsystems will be in the canonical state, as predicted by statistical mechanics. Finally we show that pseudo-random states are useless for measurement-based quantum computation.

scholarly journals Symmetry resolved entanglement in integrable field theories via form factor bootstrap

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Dávid X. Horváth ◽  
Pasquale Calabrese
Keyword(s):  
Form Factor ◽  
Integrable Field Theories ◽  
Field Theories ◽  
Von Neumann Entropy ◽  
Matrix Elements ◽  
Von Neumann ◽  
Bootstrap Approach ◽  
Complete Computation ◽  
Twist Fields ◽  
Integrable Field

Abstract We consider the form factor bootstrap approach of integrable field theories to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are determined in an intuitive way and their solution is presented for the massive Ising field theory and for the genuinely interacting sinh-Gordon model, both possessing a ℤ2 symmetry. The solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. The issue of symmetry resolution for discrete symmetries is also discussed. We show that entanglement equipartition is generically expected and we identify the first subleading term (in the UV cutoff) breaking it. We also present the complete computation of the symmetry resolved von Neumann entropy for an interval in the ground state of the paramagnetic phase of the Ising model. In particular, we compute the universal functions entering in the charged and symmetry resolved entanglement.

Galileo Unbound

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Free Fall ◽  
The Sun ◽  
Quantum Field ◽  
Many Worlds ◽  
Quantum Particles ◽  
Light Rays ◽  
History Of ◽  
And Control ◽  
The Universe ◽  
Insight Into

Galileo Unbound: A Path Across Life, The Universe and Everything traces the journey that brought us from Galileo’s law of free fall to today’s geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman’s dilemma of quantum particles taking all paths at once—setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

scholarly journals The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 124
Author(s):  
Vadim Monakhov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Symmetry Breaking ◽  
Momentum Space ◽  
Quantum Field ◽  
Conjugation Operator ◽  
Dirac Sea ◽  
Canonical Anticommutation Relations ◽  
The Universe ◽  
Dirac Conjugation

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

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