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One electron atoms in both a squeezed vacuum and a magnetic field via path integral methods

EUROPEAN PHYSICAL JOURNAL D 2001年第1期15卷 19-23页

作者： Thrapsaniotis, EG 52 Vianou st. 13671 Athens Aharnes Greece GR

In the present paper we study the dynamics of one-electron atoms: in the presence of both a linearly polarized squeezed vacuum and a magnetic field along the polarization vector of the photonic field. We adopt the dipole approximation and approach the problem via path integral methods. After integrating over the light variables for certain initial and final squeezed vacuum states we treat the path integral over the spatial variables via Monte-Carlo methods. As an application we calculate the survival probability of the ground state of a one-electron atom for various values of the magnetic field.

关键词： Functional analytical methods path-integral methods

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Green function approximation and path integral numerical methods

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EUROPEAN PHYSICAL JOURNAL D 2000年第2期10卷 157-164页

作者： Orlandi, A Rosa-Clot, M Taddei, S Univ Modena Dipartimento Fis I-41100 Modena Italy Ist Nazl Fis Mat Sez Modena I-41100 Modena Italy Ist Nazl Fis Nucl Sez Firenze I-50125 Florence Italy Univ Florence Dipartimento Fis I-50125 Florence Italy

We evaluate the short time Green function by a series expansion of the exponent. The resulting expression allows the computation of the energy eigenvalues and eigenvectors of a quantum system with a very high precision. As an example, we show the comparison between the numerical results and the analytical solutions for harmonic and multi-well potentials both in one and two dimensions.

关键词： Computational techniques path-integral methods

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Generic topological criterion for flat bands in two dimensions

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Physical Review B 2024年第12期110卷 L121111页

作者： Alireza Parhizkar Victor Galitski Center for Computational Quantum Physics The

We show that the continuum limit of moiré graphene is described by a (2+1)-dimensional field theory of Dirac fermions coupled to two classical vector fields: a periodic gauge and a spin field. We further show that the existence of a flat band implies an effective dimensional reduction, where the time dimension is “removed.” The resulting two-dimensional Euclidean theory contains the chiral anomaly. The associated Atiyah-Singer index theorem provides a self-consistency condition for flat bands. In the Abelian limit, where the spin field is disregarded, we reproduce a periodic series of quantized magic angles known to exist in twisted bilayer graphene in the chiral limit. However, the results are not exact. If the Abelian field has zero total flux, perfectly flat bands can not exist, because of the leakage of edge states into neighboring triangular patches with opposite field orientations. We demonstrate that the non-Abelian spin component can correct this and completely flatten the bands via an effective renormalization of the Abelian component into a configuration with a nonzero total flux. We present the Abelianization of the theory where the Abelianized flat band can be mapped to that of the lowest Landau level. We show that the Abelianization corrects the values of the magic angles consistent with numerical results. We also use this criterion to prove that an external magnetic field splits the series into pairs of magnetic field-dependent magic angles associated with flat moiré-Landau bands. The topological criterion and the Abelianization procedure provide a generic practical method for finding flat bands in a variety of material systems including but not limited to moiré bilayers.

关键词： Anomalies Dirac fermions Flat bands Gauge theories Non-Abelian gauge theories Bilayer graphene Graphene Superconductors Superlattices Topological materials Twisted bilayer graphene Chiral symmetry path-integral methods Topology

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Thermodynamics of a continuum Su-Schrieffer-Heeger model

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PHYSICA B-CONDENSED MATTER 2004年第1-4期344卷 372-378页

作者： Zoli, M Univ Camerino INFM I-62032 Camerino Italy

The full partition function for an electron-phonon system described by the one dimensional Su-Schrieffer-Heeger model is exactly computed by a path integral method. Mapping the real space Hamiltonian onto the time scale we introduce a temperature dependent range hopping for the electrons. The heat capacity over temperature ratio shows an upturn at low temperatures which is a peculiar feature of the glassy state. The perturbation on the phonon subsystem due to the electron path motion are evaluated by a cumulant expansion of the phonon free energy. (C) 2003 Elsevier B.V. All rights reserved.

关键词： polarons and electron phonon interactions path-integral methods

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A path integral time-domain method for electromagnetic scattering

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2000年第4期48卷 565-573页

作者： Nevels, RD Miller, JA Miller, RE Texas A&M Univ Dept Elect Engn College Stn TX 77843 USA

A new full wave time-domain formulation for the electromagnetic field is obtained by means of a path integral, The path integral propagator is derived via a state variable approach starting with Maxwell's differential equations in tensor form. A numerical method for evaluating the path integral is presented and numerical dispersion and stability conditions are derived and numerical error is discussed. An absorbing boundary condition is demonstrated for the one-dimensional (1-D) case. It is shown that this time domain method is characterized by the unconditional stability of the path integral equations and by its ability to propagate an electromagnetic wave at the Nyquist limit, two numerical points per wavelength. As a consequence the calculated fields are not subject to numerical dispersion. Other advantages in comparison to presently popular time-domain techniques are that it avoids time interval interleaving and it does not require the methods of linear algebra such as basis function selection or matrix methods.

关键词： electromagnetic scattering path-integral methods transient scattering

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Computation of the properties of liquid neon, methane, and gas helium at low temperature by the Feynman-Hibbs approach

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JOURNAL OF CHEMICAL PHYSICS 2004年第15期121卷 7326-7331页

作者： Tchouar, N Ould-Kaddour, F Levesque, D Univ Paris 11 Phys Theor Lab F-91405 Orsay France Fac Sci USTO Dept Chim Ind Oran Algeria Univ Tlemcen Fac Sci Tilimsen 13000 Algeria

The properties of liquid methane, liquid neon, and gas helium are calculated at low temperatures over a large range of pressure from the classical molecular-dynamics simulations. The molecular interactions are represented by the Lennard-Jones pair potentials supplemented by quantum corrections following the Feynman-Hibbs approach. The equations of state, diffusion, and shear viscosity coefficients are determined for neon at 45 K, helium at 80 K, and methane at 110 K. A comparison is made with the existing experimental data and for thermodynamical quantities, with results computed from quantum numerical simulations when they are available. The theoretical variation of the viscosity coefficient with pressure is in good agreement with the experimental data when the quantum corrections are taken into account, thus reducing considerably the 60% discrepancy between the simulations and experiments in the absence of these corrections. (C) 2004 American Institute of Physics.

关键词： path-integral methods MOLECULAR-DYNAMICS TRANSPORT-COEFFICIENTS QUANTUMCORRECTIONS SELF-DIFFUSION TRIPLE POINT MONTE-CARLO HARD-SPHERE SYSTEMS EQUILIBRIUM

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Finite temperature theory of metastable anharmonic potentials

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EUROPEAN PHYSICAL JOURNAL B 2008年第2期62卷 221-231页

作者： Zoli, M. Univ Camerino Dipartimento Fis Ist Nazl Fis Mat I-62032 Camerino Italy

The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths, saddle points for the action, is derived in terms of Jacobian elliptic functions whose periodicity sets the energy-temperature correspondence. The period of the classical oscillations varies monotonically with the energy up to the sphaleron, pointing to a smooth crossover from the quantum to the activated regime. The softening of the quantum fluctuation spectrum is evaluated analytically by the theory of the functional determinants and computed at low T up to the crossover. In particular, the negative eigenvalue, causing an imaginary contribution to the partition function, is studied in detail by solving the Lame equation which governs the fluctuation spectrum. For a heavvy particle mass, the decay rate shows a remarkable temperature dependence mainly ascribable to a low lying soft mode and, approaching the crossover, it increases by a factor five over the predictions of the zero temperature theory. Just beyond the peak value, the classical Arrhenius behavior takes over. A similar trend is found studying the quartic metastable potential but the lifetime of the latter is longer by a factor ten than in a cubic potential with same parameters. Some formal analogies with noise-induced transitions in classically activated metastable systems are discussed.

关键词： Semiclassical theories and applications Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations Quantum statistical mechanics path-integral methods

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Dichroic cavity mode splitting and lifetimes from interactions with a ferromagnetic metal

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Physical Review B 2024年第16期110卷 L161102页

作者： Henning G. Hugdal Eirik Jaccheri Høydalsvik Sol H. Jacobsen Center for Quantum Spintronics Department of Physics NTNU

We study the effect of ferromagnetic metals (FM) on the circularly polarized modes of an electromagnetic cavity and show that broken time-reversal symmetry leads to a dichroic response of the cavity modes. With one spin-split band, the Zeeman coupling between the FM electrons and cavity modes leads to an anticrossing for mode frequencies comparable to the spin splitting. However, this is only the case for one of the circularly polarized modes, while the other is unaffected by the FM, allowing for the determination of the spin-splitting of the FM using polarization-dependent transmission experiments. Moreover, we show that for two spin-split bands, also the lifetimes of the cavity modes display a polarization-dependent response. The change in photon lifetimes can be understood as a suppression due to level attraction with a continuum of Stoner modes with the same wave vector. The reduced lifetime of modes of only one polarization could potentially be used to engineer and control circularly polarized cavities.

关键词： Cavity quantum electrodynamics Light-matter interaction Spintronics Ferromagnets Quantum cavities path-integral methods

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Molecular structure calculations via path integral simulations: Estimating finite-discretization errors

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EUROPEAN PHYSICAL JOURNAL D 2000年第3期10卷 353-362页

作者： Knoll, L Marx, D Max Planck Inst Kernphys D-69029 Heidelberg Germany Ruhr Univ Bochum Lehrstuhl Theoret Chem D-44780 Bochum Germany

path integral simulations are now recognized as a useful tool to determine theoretically the structure of complex molecules at finite temperatures including quantum effects. In addition to statistical errors due to incomplete sampling, also systematic errors are inherent in this procedure because of the finite discretization of the path integral. Here, useful "back of the envelope" estimates to assess the systematic errors of bond-length distribution functions are introduced. These analytical estimates are tested for two small molecules, HD+ and H-3(+), where quasi-exact benchmark data are available. The accuracy of the formulae is shown to be sufficient in order to allow for a reliable assessment of the quality of the discretization in a given simulation. The estimates will also be applicable in condensed phase path integral simulations, and the basic idea can be generalized to other observables than those presented.

关键词： path-integral methods Monte Carlo and statistical methods

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Bayesian approach to inverse quantum statistics: Reconstruction of potentials in the Feynman path integral representation of quantum theory

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EUROPEAN PHYSICAL JOURNAL B 2005年第1期46卷 41-54页

作者： Lemm, JC Uhlig, J Weiguny, A Univ Munster Inst Theoret Phys D-48149 Munster Germany

The Feynman path integral representation of quantum theory is used in a non - parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the classical and semiclassical limits and provides a unified description in terms of functional integrals: the Feynman path integral for the statistical operator and its derivative with respect to the potential, and the integration over the space of potentials for calculating the predictive density. The latter is treated in maximum a posteriori approximation, and various approximation schemes for the former are developed and discussed. A simple numerical example shows the applicability of the method.

关键词： Inference methods path-integral methods Quantum statistical mechanics

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