Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0306172 · Journal of Physics A Mathematical and General

Time correlations in a confined magnetized free-electron gas

L.G. Suttorp

Published Jul 17, 2003• 0 citations
arXivHTMLPDF

Abstract

The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the correlations is investigated, both for a perpendicular and a parallel orientation of the wall with respect to the field. The coherent and incoherent parts of the time-dependent structure function in position space are determined from an expansion in terms of the eigenfunctions of the one-particle Hamiltonian. For the bulk of the system, the intermediate scattering function and the dynamical structure factor are derived by taking successive Fourier transforms. In the vicinity of the wall the time-dependent coherent structure function is found to decay faster than in the bulk. For coinciding positions near the wall the form of the structure function turns out to be independent of the orientation of the wall. Numerical results are shown to corroborate these findings.

DOI
10.1088/0305-4470/36/30/303

Related papers

Correlations in a confined magnetized free-electron gas

M M Kettenis, L.G. Suttorp

Equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free-electron gas in the presence of a hard wall that is parallel to the field. With the help of a path-integral technique and a Green function representation, the modifications in the correlation function caused by the wall are determined both for a non-degenerate and for a completely degenerate gas. In the latter case the asymptotic behaviour of the correlation function for large position differences in the direction parallel to the wall and perpendicular to the field, is found to change from Gaussian in the bulk to algebraic near the wall.

arXiv:cond-mat/0105588•Journal of Physics A Mathematical and General•Sep 21, 2001•2 citations

Quantum mechanics in an axial magnetic field

J. Frenkel, John C. Taylor

We make three remarks about the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field (which we take to be parallel to the z-axis). First, when the field is uniform, we comment on the relation between the wave-function on the one hand if it is chosen to be an eigenstate of momentum (leaving aside the trivial z-dependence) and hence non-normalizable, and on the other hand if it is chosen to be an eigenstate of angular momentum. Second, we discuss the form of the wave-function when the magnetic field had a weak z-dependence. Finally, we make a short comment on the derivation of the diamagnetism of a free electron gas.

•Apr 30, 2004•0 citations

Correlation Energy of an Electron Gas in the Quantum Strong-Field Limit

Gerd E. Keiser, Fa Yueh Wu

The ground state of an electron gas in an intense magnetic field is studied using a wave function of the product form ${\ensuremath{\Psi}}_{0}^{B}\ensuremath{\Phi}$. The correlation factor ${\ensuremath{\Psi}}_{0}^{B}$ is taken to be the ground-state solution of a charged Bose gas and $\ensuremath{\Phi}$ a determinant of single-particle Landau states. In the quantum strong-field limit so that only the lowest Landau state is populated, the correlation energy is computed using the cluster-expansion technique and a variational determination of the boson energy. Numerical results obtained are lower than those derived under the random-phase approximation.

Physical Review A•Oct 1, 1973•9 citations

Static Pair Correlation Functions and Static Structure Factors of Unidirectional Quantum Systems

Grima Dhingra

Two of the structural functions, static pair correlation function of electrons around positively charged particles and static structure factor, have been theoretically calculated for a one dimensional quantum system with two mobile components occupying same charge density at equal temperatures.The structural functions have been investigated for their density and mass dependence.The reported values of static pair correlation function and structure factors are found to be dependent upon linear density and mass of positive components.Static pair correlation functions for a wide range of temperature, 100K≤T≤ 1500K, has also been generated theoretically.A variation, though diminutive, with temperature has been observed.

International Journal of Scientific Research in Physics and Applied Sciences•Jun 30, 2019•0 citations

Transport and real-time dynamics in one-dimensional quantum magnets and ultra-cold atomic gases

Langer, Stephan Markus

The goal of this thesis is to study the transport properties and real-time dynamics of quantum magnets and ultra-cold atomic gases in one spatial dimension using numerical methods. The focus will be on the discussion of diffusive versus ballistic dynamics along with a detailed analysis of characteristic velocities in ballistic regimes. For the simulation of time-dependent density profiles we use the adaptive time-dependent density matrix renormalization group (DMRG). This numerical method allows for the simulation of time-dependent wave functions close to as well as far from equilibrium in a controlled manner. The studies of one-dimensional quantum magnets are partially motivated by the experimental evidence for a highly anisotropic and for insulators comparably high thermal conductivity of certain cuprates. We use linear response theory to study transport coefficients at arbitrary temperatures by diagonalizing small systems exactly and then calculating the current-current correlation functions. As first application we discuss the spin transport in the spin-$1/2$ Heisenberg chain with anisotropic exchange interactions (XXZ-chain). The second application of exact diagonalization, here in combination with time-dependent DMRG, is a discussion of the transverse components of the current-current correlation function. While usually only a Zeeman field is considered in the theory of transport coefficients, we here investigate the dynamic induced by an additional transverse magnetic field. We find that in this scenario the current-current correlation function exhibits coherent oscillations. In addition a second non-trivial frequency, different from the one expected from the usual Larmor precession, emerges and is studied varying temperature and field. Finally we calculate the frequency-dependent spin and heat conductivity of dimerized spin chains in a magnetic field. Motivated by the recent experimental studies of the phase diagram of C$_5$H$_{12}$N$_2$CuBr$_4$ we take the dimerized chain as a minimal model that exhibits features of the low-temperature region of the observed phase diagram. As a main result, the spin and heat conductivity obtained from linear response theory are enhanced in the field-induced gapless phase. The last application in the field of one-dimensional quantum magnets is the simulation of time-dependent energy-density wave-packets close to as well as far from equilibrium using the time-dependent density renormalization group. The main results are ballistic energy dynamics independently of how far out-of-equilibrium the initial state is and a detailed understanding of the average expansion velocity. The applications in the field of ultra-cold atomic gases focus on the sudden expansion of an initially trapped gas into an empty optical lattice. This setup was recently realized in an experiment performed by U. Schneider {\it et al.} and discussed in the context of electronic transport in the two-dimensional and the three-dimensional Fermi-Hubbard model. Here we investigate the sudden expansion of three different setups: For the expansion of a spin-balanced cloud of fermions, we identify the ballistic regime, and therein investigate the average expansion velocity of the cloud. As a main result the expansion velocity is determined by a small subset of the initial condition over a wide range of parameters. For instance, the Mott-insulating phase of the Hubbard model is characterized by a constant expansion velocity independently of the strength of the interaction. In the case of spinless bosons, we study the expansion from initial states that have a fixed particle number per lattice site and a certain concentration of defects. We study the expansion velocity as a function of interaction strength and investigate whether the time-dependent momentum distribution functions indicate a dynamical quasi-condensation. The last example is the sudden expansion of a spin-polarized gas of fermions in the presence of attractive interactions. This study is motivated by current effort to experimentally detect the Fulde-Ferrell-Larkin-Ovchinnikov state. Our results for the time-dependent momentum distribution functions and the wave-function of the pair condensate suggest that the signatures of the FFLO state vanish quickly, yet a stationary form of the momentum distribution also emerges fast. The latter is shown to be determined by the initial conditions, which might eventually allow for an indirect detection of the FFLO phase.

•Jan 1, 2012•0 citations

Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum

Jonas Richter, Fengping Jin, Lars Knipschild +5 more

The dynamics of magnetization and energy densities are studied in the two-leg spin-$1/2$ ladder. Using an efficient pure-state approach based on the concept of typicality, we calculate spatiotemporal correlation functions for large systems with up to 40 lattice sites. In addition, two subsequent Fourier transforms from real to momentum space as well as from the time to frequency domain yield the respective dynamical structure factors. Summarizing our main results, we unveil the existence of genuine diffusion for both spin and energy. In particular, this finding is based on four distinct signatures which can all be equally well detected: (i) Gaussian density profiles, (ii) time-independent diffusion coefficients, (iii) exponentially decaying density modes, and (iv) Lorentzian line shapes of the dynamical structure factor. The combination of (i)--(iv) provides a comprehensive picture of high-temperature dynamics in this archetypal nonintegrable quantum model.

arXiv:1811.02806•Physical review. B./Physical review. B•Apr 23, 2019•23 citations
The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the correlations is investigated, both for a perpendicular and a parallel orientation of the wall with respect to the field. The coherent and incoherent parts of the time-dependent structure function in position space are determined from an expansion in terms of the eigenfunctions of the one-particle Hamiltonian. For the bulk of the system, the intermediate scattering function and the dynamical structure factor are derived by taking successive Fourier transforms. In the vicinity of the wall the time-dependent coherent structure function is found to decay faster than in the bulk. For coinciding positions near the wall the form of the structure function turns out to be independent of the orientation of the wall. Numerical results are shown to corroborate these findings.
Equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free-electron gas in the presence of a hard wall that is parallel to the field. With the help of a path-integral technique and a Green function representation, the modifications in the correlation function caused by the wall are determined both for a non-degenerate and for a completely degenerate gas. In the latter case the asymptotic behaviour of the correlation function for large position differences in the direction parallel to the wall and perpendicular to the field, is found to change from Gaussian in the bulk to algebraic near the wall.
We make three remarks about the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field (which we take to be parallel to the z-axis). First, when the field is uniform, we comment on the relation between the wave-function on the one hand if it is chosen to be an eigenstate of momentum (leaving aside the trivial z-dependence) and hence non-normalizable, and on the other hand if it is chosen to be an eigenstate of angular momentum. Second, we discuss the form of the wave-function when the magnetic field had a weak z-dependence. Finally, we make a short comment on the derivation of the diamagnetism of a free electron gas.
The ground state of an electron gas in an intense magnetic field is studied using a wave function of the product form ${\ensuremath{\Psi}}_{0}^{B}\ensuremath{\Phi}$. The correlation factor ${\ensuremath{\Psi}}_{0}^{B}$ is taken to be the ground-state solution of a charged Bose gas and $\ensuremath{\Phi}$ a determinant of single-particle Landau states. In the quantum strong-field limit so that only the lowest Landau state is populated, the correlation energy is computed using the cluster-expansion technique and a variational determination of the boson energy. Numerical results obtained are lower than those derived under the random-phase approximation.
Two of the structural functions, static pair correlation function of electrons around positively charged particles and static structure factor, have been theoretically calculated for a one dimensional quantum system with two mobile components occupying same charge density at equal temperatures.The structural functions have been investigated for their density and mass dependence.The reported values of static pair correlation function and structure factors are found to be dependent upon linear density and mass of positive components.Static pair correlation functions for a wide range of temperature, 100K≤T≤ 1500K, has also been generated theoretically.A variation, though diminutive, with temperature has been observed.
The goal of this thesis is to study the transport properties and real-time dynamics of quantum magnets and ultra-cold atomic gases in one spatial dimension using numerical methods. The focus will be on the discussion of diffusive versus ballistic dynamics along with a detailed analysis of characteristic velocities in ballistic regimes. For the simulation of time-dependent density profiles we use the adaptive time-dependent density matrix renormalization group (DMRG). This numerical method allows for the simulation of time-dependent wave functions close to as well as far from equilibrium in a controlled manner. The studies of one-dimensional quantum magnets are partially motivated by the experimental evidence for a highly anisotropic and for insulators comparably high thermal conductivity of certain cuprates. We use linear response theory to study transport coefficients at arbitrary temperatures by diagonalizing small systems exactly and then calculating the current-current correlation functions. As first application we discuss the spin transport in the spin-1/21/21/2 Heisenberg chain with anisotropic exchange interactions (XXZ-chain). The second application of exact diagonalization, here in combination with time-dependent DMRG, is a discussion of the transverse components of the current-current correlation function. While usually only a Zeeman field is considered in the theory of transport coefficients, we here investigate the dynamic induced by an additional transverse magnetic field. We find that in this scenario the current-current correlation function exhibits coherent oscillations. In addition a second non-trivial frequency, different from the one expected from the usual Larmor precession, emerges and is studied varying temperature and field. Finally we calculate the frequency-dependent spin and heat conductivity of dimerized spin chains in a magnetic field. Motivated by the recent experimental studies of the phase diagram of C5_55​H12_{12}12​N2_22​CuBr4_44​ we take the dimerized chain as a minimal model that exhibits features of the low-temperature region of the observed phase diagram. As a main result, the spin and heat conductivity obtained from linear response theory are enhanced in the field-induced gapless phase. The last application in the field of one-dimensional quantum magnets is the simulation of time-dependent energy-density wave-packets close to as well as far from equilibrium using the time-dependent density renormalization group. The main results are ballistic energy dynamics independently of how far out-of-equilibrium the initial state is and a detailed understanding of the average expansion velocity. The applications in the field of ultra-cold atomic gases focus on the sudden expansion of an initially trapped gas into an empty optical lattice. This setup was recently realized in an experiment performed by U. Schneider {\it et al.} and discussed in the context of electronic transport in the two-dimensional and the three-dimensional Fermi-Hubbard model. Here we investigate the sudden expansion of three different setups: For the expansion of a spin-balanced cloud of fermions, we identify the ballistic regime, and therein investigate the average expansion velocity of the cloud. As a main result the expansion velocity is determined by a small subset of the initial condition over a wide range of parameters. For instance, the Mott-insulating phase of the Hubbard model is characterized by a constant expansion velocity independently of the strength of the interaction. In the case of spinless bosons, we study the expansion from initial states that have a fixed particle number per lattice site and a certain concentration of defects. We study the expansion velocity as a function of interaction strength and investigate whether the time-dependent momentum distribution functions indicate a dynamical quasi-condensation. The last example is the sudden expansion of a spin-polarized gas of fermions in the presence of attractive interactions. This study is motivated by current effort to experimentally detect the Fulde-Ferrell-Larkin-Ovchinnikov state. Our results for the time-dependent momentum distribution functions and the wave-function of the pair condensate suggest that the signatures of the FFLO state vanish quickly, yet a stationary form of the momentum distribution also emerges fast. The latter is shown to be determined by the initial conditions, which might eventually allow for an indirect detection of the FFLO phase.
The dynamics of magnetization and energy densities are studied in the two-leg spin-1/21/21/2 ladder. Using an efficient pure-state approach based on the concept of typicality, we calculate spatiotemporal correlation functions for large systems with up to 40 lattice sites. In addition, two subsequent Fourier transforms from real to momentum space as well as from the time to frequency domain yield the respective dynamical structure factors. Summarizing our main results, we unveil the existence of genuine diffusion for both spin and energy. In particular, this finding is based on four distinct signatures which can all be equally well detected: (i) Gaussian density profiles, (ii) time-independent diffusion coefficients, (iii) exponentially decaying density modes, and (iv) Lorentzian line shapes of the dynamical structure factor. The combination of (i)--(iv) provides a comprehensive picture of high-temperature dynamics in this archetypal nonintegrable quantum model.