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1.
An extended analytic approach is considered for optical Bloch equations in the two level atom interacting with laser light.
The separation approach of coupled differential equations is always possible with a sequence of special transformation into
the Riccati nonlinear differential equation. The conditions that permit an exact solutions of three coupled system are extracted
in a natural manner. The case of sodium atom moving along the axis of a monochromatic wave is treated in some details including
a discussion on the radiation pressure forces exerted by laser light in the transient regime.
PACS numbers: 32.80.Pj, 42.50.Vk, 42.50.Hz, 42.50.Lc. 相似文献
2.
Jaume Haro 《International Journal of Theoretical Physics》2007,46(4):951-971
The energy of the evolved vacuum state is calculated. From a frequency cut-off regularisation the divergent terms are separated
and, in the 1 + 1 dimensional case they are removed with a mass renormalisation of the moving boundary. A renormalisation
of the external force is also needed in 3 + 1 dimensions.
PACS Subject Classifications: 42.50.Lc, 03.70.+k, 11.10.Ef. 相似文献
3.
Various aspects of dissipative and nondissipative decoherence of Rabi oscillations are discussed in the context of field quantization
in alternative representations of CCR. Theory is confronted with experiment, and a possibility of more conclusive tests is
analyzed.
PACS numbers: 42.50.Pq, 42.50.Xa, 03.70.+k 相似文献
4.
A thin layer of the event horizon vicinity to the two-dimension black hole with a global monopole is considered as a system
of the Casimir type. The energy-momentum tensor is derived in Boulware vacuum, Hartle-Hawking vacuum and Unruh vacuum respectively.
The values are derived in the massless scalar field which satisfies the Dirichlet boundary conditions. Using the Wald's axioms,
the result is got which is the same with the one derived by the usual regularized methods. Meanwhile, the energy, energy density,
and pressure acting on the boundaries at the asymptotically flat background also are calculated too, and from the energy,
Casimir force is derived. The Casimir energy and Casimir force are compared respectively in the background before and after
radiation.
PACS: 42.50.Lc. 相似文献
5.
M. Cini E. Perfetto G. Stefanucci 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,20(1):91-103
We introduce a local formalism, in terms of eigenstates of number operators, having well defined point symmetry, to solve the Hubbard model at
weak coupling on a N
×
N square lattice (for even N). The key concept is that of W
= 0 states, that are the many-body eigenstates of the kinetic energy with vanishing Hubbard repulsion. At half filling, the wave
function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. Further, we
state a general theorem which allows to find all the W
= 0 pairs (two-body W
= 0 singlet states). We show that, in special cases, this assigns the ground state symmetries at least in the weak coupling regime.
The N
= 4 case is discussed in detail. To study the doped half filled system, we enhance the group theory analysis of the 4×4 Hubbard model introducing an Optimal Group which explains all the degeneracies in the one-body and many-body spectra. We
use the Optimal Group to predict the possible ground state symmetries of the 4×4 doped antiferromagnet by means of our general theorem and the results are in agreement with exact diagonalization data. Then
we create W
= 0
electron pairs over the antiferromagnetic state. We show analitycally that the effective interaction between the electrons of the
pairs is attractive and forms bound states. Computing the corresponding binding energy we are able to definitely predict the
exact ground state symmetry.
Received 24 October 2000 相似文献
6.
A generalized two-mode harmonic oscillator model is investigated within the framework of its general dynamical algebra so(3,2). Two types of eigenstates, formulated as extended su(1,1), su(2) squeezed number states are found respectively. The nonadiabatic Berrys phase for this system with the cranked time-dependent Hamiltonian is also given.Received: 16 January 2004, Published online: 10 August 2004PACS:
42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements - 03.65.Fd Algebraic methods - 03.65.Vf Phases: geometric; dynamic or topological 相似文献
7.
J.M. Cerveró A. Rodrıguez 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(2):239-251
We present the exact diagonalization of the Schr?dinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with
a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main
physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These
quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow
unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates
in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model
many of the salient features expected in a quantum wire are well reproduced.
Received 24 June 2002 Published online 29 November 2002 相似文献
8.
9.
Zohar Nussinov 《哲学杂志》2013,93(18):1509-1566
We apply microcanonical ensemble considerations to suggest that, whenever it may thermalise, a general disorder-free many-body Hamiltonian of a typical atomic system has solid-like eigenstates at low energies and fluid-type (and gaseous, plasma) eigenstates associated with energy densities exceeding those present in the melting (and, respectively, higher energy) transition(s). In particular, the lowest energy density at which the eigenstates of such a clean many body atomic system undergo a non-analytic change is that of the melting (or freezing) transition. We invoke this observation to analyse the evolution of a liquid upon supercooling (i.e. cooling rapidly enough to avoid solidification below the freezing temperature). Expanding the wavefunction of a supercooled liquid in the complete eigenbasis of the many-body Hamiltonian, only the higher energy liquid-type eigenstates contribute significantly to measurable hydrodynamic relaxations (e.g. those probed by viscosity) while static thermodynamic observables become weighted averages over both solid- and liquid-type eigenstates. Consequently, when extrapolated to low temperatures, hydrodynamic relaxation times of deeply supercooled liquids (i.e. glasses) may seem to diverge at nearly the same temperature at which the extrapolated entropy of the supercooled liquid becomes that of the solid. In this formal quantum framework, the increasingly sluggish (and spatially heterogeneous) dynamics in supercooled liquids as their temperature is lowered stems from the existence of the single non-analytic change of the eigenstates of the clean many-body Hamiltonian at the equilibrium melting transition present in low energy solid-type eigenstates. We derive a single (possibly computable) dimensionless parameter fit to the viscosity and suggest other testable predictions of our approach. 相似文献
10.
Bill Poirier 《Foundations of Physics》2001,31(11):1581-1610
In an earlier article [Found. Phys.
30, 1191 (2000)], a quasiclassical phase space approximation for quantum projection operators was presented, whose accuracy increases in the limit of large basis size (projection subspace dimensionality). In a second paper [J. Chem. Phys.
111, 4869 (1999)], this approximation was used to generate a nearly optimal direct-product basis for representing an arbitrary (Cartesian) quantum Hamiltonian, within a given energy range of interest. From a few reduced-dimensional integrals, the method determines the optimal 1D marginal Hamiltonians, whose eigenstates comprise the direct-product basis. In the present paper, this phase space optimized direct-product basis method is generalized to incorporate non-Cartesian coordinate spaces, composed of radii and angles, that arise in molecular applications. Analytical results are presented for certain standard systems, including rigid rotors, and three-body vibrators. 相似文献
11.
G.A. Intronati P.I. Tamborenea D. Weinmann R.A. Jalabert 《Physica B: Condensed Matter》2012,407(16):3252-3255
We study numerically the effects of an extrinsic spin–orbit interaction on the model of electrons in n-doped semiconductors of Matsubara and Toyozawa (MT). We focus on the analysis of the density of states (DOS) and the inverse participation ratio (IPR) of the spin–orbit perturbed states in the MT set of energy eigenstates in order to characterize the eigenstates with respect to their extended or localized nature. The finite sizes that we are able to consider necessitate an enhancement of the spin–orbit coupling strength in order to obtain a meaningful perturbation. The IPR and DOS are then studied as a function of the enhancement parameter. 相似文献
12.
The influence of interdiffusion on eigenstates in an interdiffusion-induced GaAs/AlxGa1-xAs single-quantum-well structure is analysed numerically by the finite element method. In this approach, the confinement potential profile of the interdiffused quantum well structure is nonlinear and is modelled by an error function and, in particular, the nature of the effective mass of an electron is considered. The results show that the number of eigenstates and energy levels varies with the extent of the interdiffusion. Numerical results for the quasi-bound states in the quantum well structure with an applied electric field are also presented. 相似文献
13.
The spectrum of energy and eigenstates of an hybrid cavity optomechanical system, where a cavity field mode interacts with a mechanical mode of a vibrating end mirror via radiation pressure and with a two level atom via electric dipole interaction are investigated. In the spirit of approximations developed for the quantum Rabi model beyond rotating-wave approximation (RWA), the so-called generalized RWA (GRWA) to diagonalize the tripartite Hamiltonian for arbitrary large couplings is implemented. Notably, the GRWA approach still allows to rewrite the hybrid Hamiltonian in a bipartite form, like a Rabi model with dressed atom-field states (polaritons) coupled to mechanical modes through reparametrized coupling strength and Rabi frequency. A more accurate energy spectrum for a wide range of values of the atom-photon and photon–phonon couplings, when compared to the RWA results is found. The fidelity between the numerical eigenstates and its approximated counterparts is also calculated. The degree of polariton-phonon entanglement of the eigenstates presents a non-monotonic behavior as the atom-photon coupling varies, in contrast to the characteristic monotonic increase in the RWA treatment. 相似文献
14.
Quench dynamics of two one-dimensional harmonically trapped bosons bridging attraction and repulsion
ABSTRACTWe unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analysed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity. Resorting to the fidelity spectrum and the eigenspectrum we identify the dominant eigenstates of the system that govern the dynamics. Monitoring the dynamics of the above-mentioned observables we provide signatures of the energetically higher-lying states triggered by the quench. 相似文献
15.
16.
M. Lüscher 《Communications in Mathematical Physics》1986,105(2):153-188
The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L. The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner. At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example). 相似文献
17.
We show numerically that a finite isolated cluster of interacting spins 1/2 exhibits a surprising nonthermal statistics when subjected to a series of small nonadiabatic perturbations by an external magnetic field. The resulting occupations of energy eigenstates are significantly higher than the thermal ones on both the low and the high ends of the energy spectra. This behavior semiquantitatively agrees with the statistics predicted for the so-called "quantum microcanonical" ensemble, which includes all possible quantum superpositions with a given energy expectation value. Our findings also indicate that the eigenstates of the perturbation operators are generically localized in the energy basis of the unperturbed Hamiltonian. This kind of localization possibly protects the thermal behavior in the macroscopic limit. 相似文献
18.
T. Cheng 《Annals of Physics》2010,325(2):265-286
We study the spectral and dynamical properties of a simplified model system of interacting fermions and bosons. The spatial discretization and an effective truncation of the Hilbert space permit us to compute the distribution of the bare fermions and bosons in the energy eigenstates of the coupled system. These states represent the physical particles and are used to examine the validity of the analytical predictions by perturbation theory and by the Greenberg-Schweber approximation that assumes all fermions are at rest. As an example of our numerical framework, we examine how a bare electron can trigger the creation of a cloud of virtual bosons around. We relate this cloud to the properties of the associated energy eigenstates. 相似文献
19.
Donald H. Kobe 《International Journal of Theoretical Physics》1982,21(8-9):685-702
The gauge invariance of the Dirac equation is reviewed and gauge-invariant operators are defined. The Hamiltonian is shown
to be gauge dependent, and an energy operator is defined which is gauge invariant. Gauge-invariant operators corresponding
to observables are shown to satisfy generalized Ehrenfest theorems. The time rate of change of the expectation value of the
energy operator is equal to the expectation value of the power operator. The virial theorem is proved for a relativistic electron
in a time-varying electromagnetic field. The conventional approach to probability amplitudes, using the eigenstates of the
unperturbed Hamiltonian, is shown in general to be gauge dependent. A gaugeinvariant procedure for probability amplitudes
is given, in which eigenstates of the energy operator are used. The two methods are compared by applying them to an electron
in a zero electromagnetic field in an arbitrary gauge.
Presented at the Dirac Symposium, Loyola University, New Orleans, May 1981. 相似文献
20.
We propose a method to investigate the energy eigenvalue problem and corresponding yrast line for harmonically trapped interacting N-boson systems. This method is particularly simple and effective to obtain the explicit analytical expressions of low-L energy eigenstates with L denoting systems' total angular momentum but with an arbitrarily large N. We have derived the explicit analytical results for L = 0,1,....,9 and discussed the yrast line for these low- L energy eigenstates. 相似文献