Coupled-channels density-matrix approach to low-energy nuclear collision dynamics: A technique for quantifying quantum decoherence effects on reaction observables

A. Díaz-Torres

arXiv:1010.3611Physical Review CNov 29, 201025 citations

arXiv:2009.01917 · Physical review. D/Physical review. D.

Quantum Boltzmann equation for fermions: An attempt to calculate the NMR relaxation and decoherence times using quantum field theory techniques

Hassan Manshouri, Ahmad Hoseinpour, Moslem Zarei

Published May 21, 2021• 5 citations

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Abstract

DOI: 10.1103/physrevd.103.096020

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Quantum Boltzmann equation for fermions: an attempt to calculate the NMR relaxation times using the quantum field theory techniques

Hassan Manshouri, Ahmad Hoseinpour, Moslem Zarei

Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of a system of nucleons. Using the quantum field theory tools for constructing the density matrix operators and calculating the interactions is the main advantage of this equation. The right-hand side of this equation involves forward scattering and usual collision terms. As examples of application, we calculate the standard Bloch equations for the nucleon system in the presence of a constant and an oscillating magnetic field from the forward scattering term. We find the longitudinal and transverse relaxation times from the collision term by considering the nucleon-nucleon scattering.Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of a system of nucleons. Using the quantum field theory tools for constructing the density matrix operators and calculating the interactions is the main advantage of this equation. The right-hand side of this equation involves forward scattering and usual collision terms. As examples of application, we calculate the standard Bloch equations for the nucleon system in the presence of a constant and an oscillating magnetic field from the forward scattering term. We find the longitudinal and transverse relaxation times from the collision term by considering the nucleon-nucleon scattering.

Sep 3, 20201 citation

The Density Matrix

The density matrix is a useful concept which will allow one to deal with a large collection of spinors with a statistical distribution at time t = 0 and follow their time evolution by tracking the time evolution of a new operator (the density matrix). This will require the extension of the Bloch sphere to the Bloch ball concept, in which the vector representing the collection of spinors will be able to reach points in the interior of the Bloch sphere as a function of time. This requires the inclusion of damping and scattering mechanisms representing interactions among spinors, and also their interactions with the environment. The phenomenological equations allowing a description of these relaxation mechanisms are known as Bloch’s equations. They are introduced here through a connection to the Bloch sphere and Bloch ball concepts. The longitudinal and transverse relaxation times, T1 and T2, respectively, are also introduced and some numerical examples (results of Monte-Carlo simulations) are presented to illustrate their physical meaning.The density matrix is a useful concept which will allow one to deal with a large collection of spinors with a statistical distribution at time t = 0 and follow their time evolution by tracking the time evolution of a new operator (the density matrix). This will require the extension of the Bloch sphere to the Bloch ball concept, in which the vector representing the collection of spinors will be able to reach points in the interior of the Bloch sphere as a function of time. This requires the inclusion of damping and scattering mechanisms representing interactions among spinors, and also their interactions with the environment. The phenomenological equations allowing a description of these relaxation mechanisms are known as Bloch’s equations. They are introduced here through a connection to the Bloch sphere and Bloch ball concepts. The longitudinal and transverse relaxation times, T1 and T2, respectively, are also introduced and some numerical examples (results of Monte-Carlo simulations) are presented to illustrate their physical meaning.

CRC Press eBooksSep 18, 20150 citations

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Supriyo Bandyopadhyay, Marc Cahay

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On a derivation of the Boltzmann equation in Quantum Field Theory

Gregor Leiler

The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equation (HE). A natural question then arises whether it is possible to derive the BE from physical first principles, i.e. the Heisenberg equation in Quantum Field Theory. In this work we attempted to answer this question and succeeded in deriving the BE from the HE, thus further clarifying its conceptual status. In particular, the results we have obtained are as follows. Firstly, we establish the non-perturbative validity of what we call the "pre-Boltzmann equation". The crucial point here is that this latter equation is equivalent to the Heisenberg equation. Secondly, we proceed to consider various limits of the pre-Boltzmann equation, namly the "low density" and the "weak coupling" limits, to obtain two equations that can be considered as generalizations of the BE. These limits are always taken together with the "long time" limit, which allows us to interpret the BE as an appropriate long time limit of the HE. The generalization we obtain consists in additional "correction" terms to the usual Boltzmann collision factor, and can be associated to multiple particle scattering. Unlike the pre-Boltzmann equation, these latter results are only valid pertubatively. Finally, we briefly consider the possibility to extend these results beyond said limits and outline some important aspects in this case.The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equation (HE). A natural question then arises whether it is possible to derive the BE from physical first principles, i.e. the Heisenberg equation in Quantum Field Theory. In this work we attempted to answer this question and succeeded in deriving the BE from the HE, thus further clarifying its conceptual status. In particular, the results we have obtained are as follows. Firstly, we establish the non-perturbative validity of what we call the "pre-Boltzmann equation". The crucial point here is that this latter equation is equivalent to the Heisenberg equation. Secondly, we proceed to consider various limits of the pre-Boltzmann equation, namly the "low density" and the "weak coupling" limits, to obtain two equations that can be considered as generalizations of the BE. These limits are always taken together with the "long time" limit, which allows us to interpret the BE as an appropriate long time limit of the HE. The generalization we obtain consists in additional "correction" terms to the usual Boltzmann collision factor, and can be associated to multiple particle scattering. Unlike the pre-Boltzmann equation, these latter results are only valid pertubatively. Finally, we briefly consider the possibility to extend these results beyond said limits and outline some important aspects in this case.

Jan 1, 20100 citations

Quantum Kinetic Theory for Spin Fermion Systems

Peng Mei

In this thesis, the main goal is to study the kinetic dynamics based on Hubbard model in dimensions d>2. We analyse rigorously some basic properties of the dynamics in the following scaling limit. As the coupling constant converges to zero, we rescale the time variable to capture the slow dynamics: we let coupling constant go to zero, time to infinity in such a way that the product of square of the coupling constant and time has a finite limit. The main ingredient of the kinetic limit is that, combining some basic ideas of scattering theory (long time scale) and perturbation theory (small coupling parameter), it automatically selects from the microscopic dynamics some dominating terms. This gives rise to a new description of time evolution (given by quantum Boltzmann equation), whose form can already be postulated from the second order perturbative expansion. The limit equation is expected to capture nontrivial information about the original system. Besides the weak coupling dynamics, we also discuss two complementary results in related Fermion systems.In this thesis, the main goal is to study the kinetic dynamics based on Hubbard model in dimensions d>2. We analyse rigorously some basic properties of the dynamics in the following scaling limit. As the coupling constant converges to zero, we rescale the time variable to capture the slow dynamics: we let coupling constant go to zero, time to infinity in such a way that the product of square of the coupling constant and time has a finite limit. The main ingredient of the kinetic limit is that, combining some basic ideas of scattering theory (long time scale) and perturbation theory (small coupling parameter), it automatically selects from the microscopic dynamics some dominating terms. This gives rise to a new description of time evolution (given by quantum Boltzmann equation), whose form can already be postulated from the second order perturbative expansion. The limit equation is expected to capture nontrivial information about the original system. Besides the weak coupling dynamics, we also discuss two complementary results in related Fermion systems.

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Coupled-channels density-matrix approach to low-energy nuclear collision dynamics: A technique for quantifying quantum decoherence effects on reaction observables

A. Díaz-Torres

The coupled-channels density-matrix technique for nuclear reaction dynamics, which is based on the Liouville-von Neumann equation with Lindblad dissipative terms, is developed with the inclusion of full angular momentum couplings. It allows a quantitative study of the role and importance of quantum decoherence in nuclear scattering. Formulas of asymptotic observables that can reveal effects of quantum decoherence are given. A method for extracting energy-resolved scattering information from the time-dependent density matrix is introduced. As an example, model calculations are carried out for the low-energy collision of the $^{16}\mathrm{O}$ projectile on the $^{154}\mathrm{Sm}$ target.The coupled-channels density-matrix technique for nuclear reaction dynamics, which is based on the Liouville-von Neumann equation with Lindblad dissipative terms, is developed with the inclusion of full angular momentum couplings. It allows a quantitative study of the role and importance of quantum decoherence in nuclear scattering. Formulas of asymptotic observables that can reveal effects of quantum decoherence are given. A method for extracting energy-resolved scattering information from the time-dependent density matrix is introduced. As an example, model calculations are carried out for the low-energy collision of the $^{16}\mathrm{O}$ projectile on the $^{154}\mathrm{Sm}$ target.

arXiv:1010.3611Physical Review CNov 29, 201025 citations

^{16}\mathrm{O}

projectile on the

^{154}\mathrm{Sm}

target.