scholarly journals Time evolution of Heisenberg operators of nuclei and electrons of QED system based on field theory

2013 ◽  
Vol 454 ◽  
pp. 012052 ◽  
Author(s):  
Masato Senami ◽  
Toshihide Miyazato ◽  
Soujirou Takada ◽  
Yuji Ikeda ◽  
Akitomo Tachibana
Keyword(s):  
Field Theory ◽  
Time Evolution ◽  
Heisenberg Operators

scholarly journals Non-Equilibrium Quantum Electrodynamics in Open Systems as a Realizable Representation of Quantum Field Theory of the Brain

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 43 ◽  
Author(s):  
Akihiro Nishiyama ◽  
Shigenori Tanaka ◽  
Jack A. Tuszynski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Time Evolution ◽  
Central Region ◽  
Quantum Electrodynamics ◽  
Quantum Tunneling ◽  
Evolution Equations ◽  
Open Systems ◽  
Quantum Field ◽  
The Brain

We derive time evolution equations, namely the Klein–Gordon equations for coherent fields and the Kadanoff–Baym equations in quantum electrodynamics (QED) for open systems (with a central region and two reservoirs) as a practical model of quantum field theory of the brain. Next, we introduce a kinetic entropy current and show the H-theorem in the Hartree–Fock approximation with the leading-order (LO) tunneling variable expansion in the 1st order approximation for the gradient expansion. Finally, we find the total conserved energy and the potential energy for time evolution equations in a spatially homogeneous system. We derive the Josephson current due to quantum tunneling between neighbouring regions by starting with the two-particle irreducible effective action technique. As an example of potential applications, we can analyze microtubules coupled to a water battery surrounded by a biochemical energy supply. Our approach can be also applied to the information transfer between two coherent regions via microtubules or that in networks (the central region and the N res reservoirs) with the presence of quantum tunneling.

Simulating Equilibrium Behavior of Quantum Fields with Time-evolving Classical Fields

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Real Time ◽  
Time Evolution ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Quantum Fields ◽  
Equilibrium Behavior ◽  
Classical Fields

A set of field configurations (replicas) reaches equilibrium of quantum field theory after real-time evolution obeying classical equations of motion.

scholarly journals Dynamics of Dollard asymptotic variables. Asymptotic fields in Coulomb scattering

2016 ◽  
Vol 28 (01) ◽  
pp. 1650001 ◽  
Author(s):  
G. Morchio ◽  
F. Strocchi
Keyword(s):  
Field Theory ◽  
Time Evolution ◽  
Scattering Theory ◽  
Large Time ◽  
Unitary Groups ◽  
Coulomb Scattering ◽  
Repulsive Coulomb ◽  
Asymptotic Dynamics ◽  
Modified Formula ◽  
Asymptotic Fields

Generalizing Dollard’s strategy, we investigate the structure of the scattering theory associated to any large time reference dynamics [Formula: see text] allowing for the existence of Møller operators. We show that (for each scattering channel) [Formula: see text] uniquely identifies, for [Formula: see text], asymptotic dynamics [Formula: see text]; they are unitary groups acting on the scattering spaces, satisfy the Møller interpolation formulas and are interpolated by the [Formula: see text]-matrix. In view of the application to field theory models, we extend the result to the adiabatic procedure. In the Heisenberg picture, asymptotic variables are obtained as LSZ-like limits of Heisenberg variables; their time evolution is induced by [Formula: see text], which replace the usual free asymptotic dynamics. On the asymptotic states, (for each channel) the Hamiltonian can by written in terms of the asymptotic variables as [Formula: see text], [Formula: see text] the generator of the asymptotic dynamics. As an application, we obtain the asymptotic fields [Formula: see text] in repulsive Coulomb scattering by an LSZ modified formula; in this case, [Formula: see text], so that [Formula: see text] are free canonical fields and [Formula: see text].

scholarly journals Complexity growth of operators in the SYK model and in JT gravity

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Shao-Kai Jian ◽  
Brian Swingle ◽  
Zhuo-Yu Xian
Keyword(s):  
Black Hole ◽  
Computational Complexity ◽  
Time Evolution ◽  
Quantum Chaos ◽  
Linear Growth ◽  
Quantum Systems ◽  
Growth Behavior ◽  
Definition Of ◽  
Heisenberg Operators ◽  
Thermal States

Abstract The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly important to understand how these microscopically defined measures of complexity are related to notions of complexity defined in terms of a dual holographic geometry, such as complexity-volume (CV) duality. Here we study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in Jackiw-Teitelboim (JT) gravity. We compare a microscopic definition of complexity in the SYK model known as K-complexity to calculations using CV duality in JT gravity and find that both quantities show an exponential-to-linear growth behavior. We also calculate the growth of operator size under time evolution and find connections between size and complexity. While the notion of operator size saturates at the scrambling time, our study suggests that complexity, which is well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution at both early and late times.

scholarly journals Integrable Floquet QFT: Elasticity and factorization under periodic driving

2018 ◽  
Vol 5 (3) ◽  
Author(s):  
Axel Cortes Cubero
Keyword(s):  
Field Theory ◽  
Time Evolution ◽  
Infinite Number ◽  
Form Factors ◽  
Field Theories ◽  
Quantum Field ◽  
Driven Systems ◽  
Matrix Elasticity ◽  
Periodically Driven ◽  
S Matrix

In (1+1)-dimensional quantum field theory, integrability is typically defined as the existence of an infinite number of local charges of different Lorentz spin, which commute with the Hamiltonian. A well known consequence of integrability is that scattering of particles is elastic and factorizable. These properties are the basis for the bootstrap program, which leads to the exact computation of S-matrices and form factors. We consider periodically-driven field theories, whose stroboscopic time-evolution is described by a Floquet Hamiltonian. It was recently proposed by Gritsev and Polkovnikov that it is possible for some form of integrability to be preserved even in driven systems. If a driving protocol exists such that the Floquet Hamiltonian is integrable (such that there is an infinite number of local and independent charges, a subset of which are parity-even, that commute with it), we show that there are strong conditions on the stroboscopic time evolution of particle trajectories, analogous to S-matrix elasticity and factorization. We propose a new set of axioms for the time evolution of particles which outline a new bootstrap program, which can be used to identify and classify integrable Floquet protocols. We present some simple examples of driving protocols where Floquet integrability is manifest; in particular, we also show that under certain conditions, some integrable protocols proposed by Gritsev and Polkovnikov are solutions of our new bootstrap equations.

scholarly journals FIELD THEORY APPROACH TO $K^0-\overline{K^0}$ AND $B^0-\overline{B^0}$ SYSTEMS

1998 ◽  
Vol 13 (20) ◽  
pp. 3587-3600 ◽  
Author(s):  
M. BEUTHE ◽  
J. PESTIEAU ◽  
G. LÓPEZ CASTRO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cp Violation ◽  
Time Evolution ◽  
Theory Approach ◽  
Quantum Field ◽  
Unstable Particles ◽  
Mixed Systems

Quantum field theory provides a consistent framework to deal with unstable particles. We present here an approach based on field theory to describe the production and decay of unstable [Formula: see text] and [Formula: see text] mixed systems. The formalism is applied to compute the time evolution amplitudes of K0 and [Formula: see text] studied in DAPHNE and CPLEAR experiments. We also introduce a new set of parameters that describe CP violation in K→ππ decays without recourse to isospin decomposition of the decay amplitudes.

Sign in / Sign up

Export Citation Format

Share Document