A variational treatment of a two-dimensional polaron

The ground state energy of a two-dimensional (2D) Fröhlich polaron is investigated with the variational scheme recently proposed by Devreese el al. The calculation is based on a suitable modification of the strong-coupling approximation by means of which adiabatic theory extrapolates towards the weak-coupling regime.     

The Ground State Energy of the Multi-Polaron in the Strong Coupling Limit

We consider the Fröhlich N-polaron Hamiltonian in the strong coupling limit and bound its ground state energy from below. In particular, our lower bound confirms that the ground state energy of the Fröhlich polaron and the ground state energy of the associated Pekar–Tomasevich variational problem are asymptotically equal in the strong coupling limit. We generalize the operator approach that was used to prove a similar result in the N =  1 case in Lieb and Thomas (Commun. Math. Phys. 183:511–519, 1997) and apply a Feynman–Kac formula to obtain the same result for an arbitrary particle number N ≥  1.     

Energy levels of the Fröhlich polaron in a spherical quantum dot

The one-phonon variational state is suitably applied to describe the ground state and excited states of the Fröhlich polaron bound to a quantum dot. A general analytical expression for the electronic energy spectra and the polaron binding energy for different electronic subband bound states in a quantum dot is presented and discussed with reference to the parameters of a real solid.     

Magnetpolaron effect in two-dimensional anisotropic parabolic quantum dot in a perpendicular magnetic field

We study the two-dimensional weak-coupling Fr o¨hlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a new one which describes an anisotropic harmonic oscillator with new mass and trapping frequencies interacting with the same phonon bath but with different interaction form and strength. Then employing the second-order Rayleigh–Schr o¨dinger perturbation theory, we obtain the polaron correction to the ground-state energy. The magnetic field and anisotropic effects on the polaron correction to the ground-state energy are discussed.     

Polaron effects in exciton mediated resonant Raman scattering

1 LO forbidden resonant Raman scattering theory is reconsidered by including “polaron” effects in the intermediate exciton states. The Fröhlich Hamiltonian is used. Numerical calculations are carried out for TlCl and CdS: in both cases the polaron effects produce a large enhancement of the scattering cross section in the absorption region, improving the agreement between the simple hydrogenic model and the experimental results.     

Polaron effects in resonant Raman scattering

Loudon's resonant Raman scattering theory is reconsidered by including polaron effects in the intermediate electron states. The Fröhlich Hamiltonian is used to derive the polaron propagators. Numerical calculations were carried out for CdS which show that polaron effects produce a large enhancement of the scattered intensity, improving the agreement between theoretical and experimental results.     

Monotonicity of the Polaron Energy II: General Theory of Operator Monotonicity

We construct a general theory of operator monotonicity and apply it to the Fröhlich polaron hamiltonian. This general theory provides a consistent viewpoint of the Fröhlich model.     

Electron- and phonon-polaron effects in TCNQ

The effects of electron correlation and electron-optical phonon interaction were investigated in the case of the valence- and conduction bands of pure TCNQ crystals using the electron-polaron model of Toyozawa and the Fröhlich electron-phonon interaction Hamiltonian. The original Hartree-Fock bandwidths were reduced by a factor of ～3–5 to 0.034 and 0.090 eV, respectively, and the forbidden gap decreased to ～2.7 eV due to polaron formation.     

On the self-trapping of an electron due to lattice interaction

The problem of the sharpness of the polaron self-trapping transition for a single electron placed in the conduction band of an insulator and interacting with the phonons of the underlying lattice is investigated within the Fröhlich Hamiltonian. It is shown that this phenomenon depends sensitively on the lattice dimensionality, the nature of the electron-phonon coupling, the nature of the phonon dispersion; and on the discrete or the continuum nature of the applicable Hamiltonian.     

Equivalence of Two Definitions of the Effective Mass of a Polaron

Two definitions of the effective mass of a particle interacting with a quantum field, such as a polaron, are considered and shown to be equal in models similar to the Fröhlich polaron model. These are: 1. the mass defined by the low momentum energy E(P)≈E(0)+P ²/2M of the translation invariant system constrained to have momentum P and 2. the mass M of a simple particle in an arbitrary slowly varying external potential, V, described by the nonrelativistic Schrödinger equation, whose ground state energy equals that of the combined particle/field system in a bound state in the same V.     

Polaronic effects in one-dimensional quantum antidot arrays

We study the effect of polaronic corrections arising from theelectron-longitudinal optical phonon interaction on the energyspectrum of a two-dimensional electron system with a one-dimensionalperiodic antidot array geometry created by a weak electrostaticmodulation potential, and subjected to a weak magnetic fieldmodulation as well as a uniform strong perpendicular staticmagnetic field. To incorporate the effects of electron-phononinteractions within the framework of Fröhlich polaron theory, wefirst apply a displaced-oscillator type unitary transformation todiagonalise the relevant Fröhlich Hamiltonian, and we thendetermine the parameters of this transformation together with theparameter included in the electronic trial wave function . On thebasis of this technique, it has been shown that the polaroniccorrections have non-negligible effects on the electronic spectrumof a two-dimensional electron system with a quantum antidot array,since switching such an interaction results in shifting thedegeneracy restoring points of Landau levels wherein the flatbandcondition is fulfilled, thus suppressing the Weiss oscillations.     

Properties of One-Dimensional Highly Polarized Fermi Gases

Using both the exact Bethe ansatz method and the variational method, we study properties of the one-dimensional Fermi polaron. We focus on the binding energy, effective mass, momentum distributions, Tan contact and correlation functions. As the attraction increases, the impurity is more tightly bound and correlated with the surrounding particles, and the size of formed polaron decreases. In addition, compared with the Bethe ansatz method, the variational method is totally qualified to study the one-dimensional Fermi polaron. The intrinsic reason is that the number of particle-hole excitations in a Fermi sea, caused by a single impurity, is always rather small. The variational method can be well extended to other impurity systems.     

Confined and interface polarons in cylindrical nanowires in an electric field

The effect of an electric field on the basic parameters of confined and interfacepolarons in cylindrical nanowires embedded in a non-polar matrix are studied theoreticallyfor the first time. By using the Lee, Low, and Pines variational method, the analyticalexpressions for the quasi-one-dimensional Fröhlich polaron self-energy and effective massare obtained as functions of the wire radius and the strength of the electric fieldapplied perpendicular to the wire axis. We have shown that the polaron self-energy as wellas effective mass strongly depents on both the strengths of the electric field and on thewire radius. This will be taken into account in the interpretation of optical phenomenarelated to polaron motion in cylindrical nanowire, when the effect of an applied electricfield competes with the spatial quantum confinement.     

Can QCD Be a Perturbation Theory of Hadrons?

We have found that the S-matrix for atoms and hadrons depends on a gauge as the elementary particles are off mass-shell in the bound states. The S-matrix for bound states one should to construct by the projection of the Belinfante energy-momentum tensor on the Gauss equation solution for the time component with the time-axis chosen as the eigenvector of the bound state total momentum operator. We have shown that this QCD Hamiltonian determined in infrared region by the rising potential ansatz, besides the parton model in the specific gauge, contains also the nonrelativistic potential model for heavy quarkonia, the chiral Lagrangians for light quarkonia with their spectrum, the glueball physics, and the small effective coupling constant in the whole region of transversal momenta.     

Band structure of a one-dimensional Peierls-Hubbard-model

A mean field theory for a model Hamiltonian including the Fröhlich electron-phonon coupling term as well as the Hubbard electron-electron interaction term is presented.For the non antiferromagnetic case the band structure is derived; the Peierls-gap is found to be reduced but not to be quenched.     

On lower bound estimates for the energy spectrum of the Fr?hlich polaron model

Method of intermediate problems was applied to investigation of the energy spectrum of the Fr?hlich polaron model. It was shown that various infinite sequences of non-decreasing improvable lower bound estimates for the low-lying branch of the slow-moving polaron excitation energy spectral curve adjacent to the ground state energy can be derived for arbitrary values of the electron-phonon interaction constant. These bound estimates allow for explicit numerical evaluation at all orders. In conjunction with numerous well-known upper bound estimates for the energy spectral curve of the Fr?hlich polaron as a function of the interaction constant and the polaron total momentum, the aforesaid improvable lower bound estimates might provide one with virtually precise magnitude for the energy of the slow-moving polaron. Possible generalization to the case of the Fr?hlich polaron in external magnetic field is outlined.     

The Open Boundary Dynamical Elliptic Quantum Gaudin Model and Its Solution

We construct the Hamiltonians of open elliptic quantum Gaudin model and show its relation with the open boundary elliptic quantum group. We define eigenstates of the model to be Bethe vectors with η=0 of the boundary elliptic quantum group. Then, the Hamiltonian is exactly diagonalized by using the algebraic Bethe ansatz method.     

Optical conductivity by simple non-adiabatic model Hamiltonian

Two simple nonadiabatic model Hamiltonian, a generalized Rabi Hamiltonian and a caricature of the Fröhlich Hamiltonian are presented. The eigenvalue problem defined by the first is solved in Bargmann Hilbert space of analytical functions to demonstrate the methods. Results for the second are reported. Eigenvalues are given in terms of continued fractions, the eigenvectors as power series or Neumann series. The coefficients of the series are determined by simple three term recurrence relations. Using these results, the optical conductivity is calculated with Kubo's formulae. We correlate our results with experimental observations and the conventional small polaron theory.     

Variational approaches to quantum impurities: from the Fröhlich polaron to the angulon

ABSTRACT

Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron – a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon – a quasiparticle formed out of a rotating molecule in a bosonic bath. We benchmark these approaches against established theories, evaluating their accuracy as a function of the impurity-bath coupling.     

强耦合表面极化子的激发能量

采用线性组合算符方法及幺正变换方法研究了电子与表面光学(SO)声子和体纵光学(LO)声子均为强耦合的表面极化子的激发态性质.计算了体系的有效哈密顿量、振动频率和体系由基态向第一激发态跃迁所需的激发能量.