Coherent State Path Integral Approach Research Articles

Multi-level description of the vibronic dynamics of open quantum systems.

A new approximate coherent state path integral approach, which enables accurate and efficient dynamical treatment of model Hamiltonians that incorporate excited electronic states of multiple chromophores that are coupled to discrete high frequency harmonic vibrational modes, is presented. The approach is based on the mapping Hamiltonian formalism for the electronic states together with semiclassical coherent state expressions for the forward and backward propagators describing the quantum bath modes. The density matrix dynamics is propagated in the full coherent state basis for the electronic mapping and discrete vibrational mode oscillators using ensembles of weighted trajectories. An effective scheme for projecting the ensemble onto selected vibronic basis states is presented enabling the evolution of the reduced system density matrix to be monitored as well as exploring the importance of selected vibronic relaxation pathways in the multichromophore system dynamics. The approach is demonstrated for simple model Hamiltonians, and we show how this coherent state density matrix propagation approach for high frequency discrete harmonic vibrational modes can be combined with partial linearized density matrix propagation to treat an additional continuum bath of low frequency environmental modes that could, in principle, include anharmonicity.

Coherent state path integral approach to multi-time correlation functions and photon emission in a semiconductor microcavity

In this paper by using the coherent state path integral field theory approach, we calculate the grand canonical partition function of an interacting combined system in the presence of the relevant source terms. It allows us to calculate multi-time correlation functions of interacting systems without using the quantum regression theorem. Then, we investigate the power spectrum and the second-order correlation function of the emitted photons from a microcavity in the presence of excitations of a semiconductor quantum well. By using the Hubbard–Stratonovich transformation, we investigate the effects of reservoir, detuning, the Coulomb interaction and the phase space filling on the power spectrum and the second-order correlation function of the emitted photons.

A diagrammatic calculation of the energy spectrum of quantum impurity in degenerate Bose–Einstein condensate

In this paper we consider a quantum particle moving through dilute Bose–Einstein condensate at zero temperature. In our formulation the impurity particle interacts with the gas of uncoupled Bogoliubov's excitations. The perturbation theory for the Green's function of the impurity particle with respect to the impurity–condensate interaction is constructed by employing the coherent-state path integral approach. The perturbative expansion for the Green's function is resumed into the expansion for its self-energy part with the help of the diagrammatic technique developed in this work. The dispersion relation for the impurity clothed by condensate excitations is obtained and effective mass is evaluated beyond the Golden rule approximation.

Phase diagram in the quantum XY model with long-range interactions

We study the d-dimensional quantum XY model with ferromagnetic long-range interaction decaying as r-p in terms of boson operators, by employing the coherent state path integral approach. We have obtained a finite critical temperature as a function of the dimension (d) for d<p<2d. For p>2d the system becomes disordered at all temperatures. For the particular values p=3/2 and d=1 our theoretical calculations are comparable to those from Monte Carlo simulations.

Coherent-state path integral approach to the damped harmonic oscillator

The time evolution of a system of bilinearly coupled bosonic modes is investigated using the real-time path integral technique in the coherent-state representation. In order to get the stationary trajectories, the corresponding Lagrangian function is diagonalized and then the path integrals are evaluated by means of the stationary-phase method. The present treatment is applied to a dissipative harmonic oscillator within the Caldeira–Leggett model. The time evolution of the reduced density matrix in the basis of coherent states is given in simple analytic form for weak system–bath coupling, i.e. the so-called rotating-wave terms can be evaluated exactly but the non-rotating-wave terms only in a perturbative manner. The validity range of the rotating-wave approximation is discussed from the viewpoint of spectral equations. In contrast to many perturbative approaches, the bath degrees of freedom are treated explicitly. In addition, it is shown that systems without initial system–bath correlations can exhibit initial jumps in the population dynamics even for rather weak dissipation. Only with initial correlations can the classical trajectories for the system coordinate be recovered.

Quantum coherence of double-well Bose-Einstein condensates: An SU(2) coherent-state path-integral approach

Macroscopic quantum coherence of Bose gas in a double-well potential is studied, based on an SU(2) coherent-state path-integral approach. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.

Collapse of a Bose condensate with attractive interactions

We examine the Gross-Pitaevskii (GP) model for Bose-Einstein condensates in parabolic traps with attractive interactions. The decay of metastable condensates is investigated by applying the instanton formalism to the GP field theory. Employing various dynamical trial states, we derive within a coherent state path integral approach a collective coordinate description in terms of the condensate radius, in agreement with (and extending) earlier results. We then solve numerically for the complete instanton field configuration and compare with the collective coordinate approach. Adjusting only the effective mass of the collective coordinate, the two schemes are then in good agreement.

Coherent-state quantization of constrained fermion systems

The quantization of systems with first- and second-class constraints within the coherent-state path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral measures for Lagrange multipliers, which in this case are in general expected to be elements of a Grassmann algebra, is emphasized. Several examples with first- and second-class constraints are discussed.

Quantum spherical model in a random field: coherent state path integral approach

By introducing boson operators, a quantum spherical XY model in the presence of a random field has been studied by the coherent state path integral approach. The phase diagram is obtained, and the effects of the random-field fluctuations on the possibilities of the existence of a ferromagnetic phase are discussed. At the critical point, , the order parameter M describing the ordered ferromagnetic phase disappears as .Since the model is equivalent to a Bose system, we also show that the phase transition at zero temperature between the superfluid and the disordered Mott insulator phases occurs at the chemical potential , where J0 is the strength of the exchange interaction. As the temperature T goes to zero, the asymptotic behavior of the entropy and the specific heat are and , respectively.

Coherent-state quantization of constrained fermion systems

The quantization of systems with first- and second-class constraints within the coherent-state path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral measures for Lagrange multipliers, which in this case are in general expected to be elements of a Grassmann algebra, is emphasized. Several examples with first- and second-class constraints are discussed.

The ferromagnetic planar model in the presence of uniaxial single-site anisotropy

Considering spin operators in terms of boson operators, we employ the coherent state path integral approach to study the Heisenberg planar XY model in the presence of uniaxial anisotropy of the form − D( S i x ) 2 with the x direction parallel to the easy axis. The critical temperatures T c below which a ferromagnetic phase appears, are obtained as a function of the anisotropy D, and the effects of the anisotropy on the phase transition of the model are examined. We find that in the limits D = 0 and ∞, our results give finite values of the critical temperatures T c, contrary to those obtained in the molecular field approximation. We show the consistency between our results and those obtained by Lovesey and Balcar.

Berry's phase and quantum dynamics of ferromagnetic solitons.

We study spin parity effects and the quantum propagation of solitons (Bloch walls) in quasi-one dimensional ferromagnets. Within a coherent state path integral approach we derive a quantum field theory for nonuniform spin configurations. The effective action for the soliton position is shown to contain a gauge potential due to the Berry phase and a damping term caused by the interaction between soliton and spin waves. For temperatures below the anisotropy gap this dissipation reduces to a pure soliton mass renormalization. The gauge potential strongly affects the quantum dynamics of the soliton in a periodic lattice or pinning potential. For half-integer spin, destructive interference between soliton states of opposite chirality suppresses nearest neighbor hopping. Thus the Brillouin zone is halved, and for small mixing of the chiralities the dispersion reveals a surprising dynamical correlation: Two subsequent band minima belong to different chirality states of the soliton. For integer spin, the Berry phase is inoperative and a simple tight-binding dispersion is obtained. Finally it is shown that external fields can be used to interpolate continuously between the Bloch wall dispersions for half-integer and integer spin.