aqora

Introduction to simple integrable models of quantum field theory

Harald Grosse, Edwin Langmann A, Ernst Raschhofer

Springer eBooksApr 7, 20080 citations

Weak integrability breaking and full counting statistics

Stefan Groha

In this thesis two questions of equilibrium and non-equilibrium properties in many-body quantum mechanical systems are investigated. The first part is focused on probability distributions of quantum observables in many-body quantum systems. After an introduction to probability distributions, full counting statistics and the transverse field Ising model we give a brief overview over related experiments and then derive an expression for the probability distribution of the transverse field magnetization of a finite subsystem in any Gaussian state. We study the probability distribution in ground and thermal states as well as in a non-equilibrium setting after a quantum quench. We find an analytic expression for the time evolution after the quench and compare to numerics. The second part of the thesis is concerned with the stability of exact quasi-particle excitations of an integrable model after weak integrability breaking perturbations are introduced. For this we first discuss the stability of excitations in integrable systems and then give an introduction to the Heisenberg XXX-model in a magnetic field. After constructing exact excitations we calculate the decay rate in leading order perturbation theory using methods of integrability.In this thesis two questions of equilibrium and non-equilibrium properties in many-body quantum mechanical systems are investigated. The first part is focused on probability distributions of quantum observables in many-body quantum systems. After an introduction to probability distributions, full counting statistics and the transverse field Ising model we give a brief overview over related experiments and then derive an expression for the probability distribution of the transverse field magnetization of a finite subsystem in any Gaussian state. We study the probability distribution in ground and thermal states as well as in a non-equilibrium setting after a quantum quench. We find an analytic expression for the time evolution after the quench and compare to numerics. The second part of the thesis is concerned with the stability of exact quasi-particle excitations of an integrable model after weak integrability breaking perturbations are introduced. For this we first discuss the stability of excitations in integrable systems and then give an introduction to the Heisenberg XXX-model in a magnetic field. After constructing exact excitations we calculate the decay rate in leading order perturbation theory using methods of integrability.

Jan 1, 20180 citations

Non-equilibrium Aspects of Quantum Integrable Systems

Natan Andrei

APSJan 1, 20160 citations

Statistical Field theory

Thierry Giamarchi

1 Introduction 52 Equilibrium statistical mechanics 72.1 Basics; correlation functions . . 72.2 Externalﬁeld;linearresponse 82.3 Continuous systems: functional integral . . . 112.4 Examples:elasticsystems 173 Calculation of Functional Integrals 293.1 Perturbationtheory 293.2 Variationalmethod 313.3 Saddlepointmethod 324 Quantum problems; functional integral 354.1 Singleparticle 354.2 Correlation functions; Matsubara frequencies 394.3 Many degrees of freedom: example of the elastic system . . 424.4 Linkwithclassicalproblems 445 Perturbation; Linear response 475.1 Method 475.2 Analyticalcontinuation 505.3 Fluctuationdissipationtheorem 525.4 Kuboformula 535.5 Scattering, Memory function . 576 Examples 596.1 Compressibility . 596.2 Conductivity of quantum crystals; Hall eﬀect 616.3 Commensuratesystems 667 Out of equilibrium classical systems 697.1 Overdampeddynamics 697.2 Linkwiththermodynamics 707.3 MSRFormalism 7231 Introduction 52 Equilibrium statistical mechanics 72.1 Basics; correlation functions . . 72.2 Externalﬁeld;linearresponse 82.3 Continuous systems: functional integral . . . 112.4 Examples:elasticsystems 173 Calculation of Functional Integrals 293.1 Perturbationtheory 293.2 Variationalmethod 313.3 Saddlepointmethod 324 Quantum problems; functional integral 354.1 Singleparticle 354.2 Correlation functions; Matsubara frequencies 394.3 Many degrees of freedom: example of the elastic system . . 424.4 Linkwithclassicalproblems 445 Perturbation; Linear response 475.1 Method 475.2 Analyticalcontinuation 505.3 Fluctuationdissipationtheorem 525.4 Kuboformula 535.5 Scattering, Memory function . 576 Examples 596.1 Compressibility . 596.2 Conductivity of quantum crystals; Hall eﬀect 616.3 Commensuratesystems 667 Out of equilibrium classical systems 697.1 Overdampeddynamics 697.2 Linkwiththermodynamics 707.3 MSRFormalism 723

Jan 1, 20037 citations

Integrability and Out of Equilibrium Quantum Dynamics

Giuseppe Mussardo, Davide Fioretto

Jan 1, 20110 citations

Lectures on Quantum Integrability: Lattices, Symmetries and Physics

Miłosz Panfil

Springer eBooksJan 1, 20170 citations

Introduction to ‘Quantum Integrability in Out of Equilibrium Systems’

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