875 research outputs found
Dynamics of the sub-Ohmic spin-boson model: a time-dependent variational study
The Dirac-Frenkel time-dependent variation is employed to probe the dynamics
of the zero temperature sub-Ohmic spin-boson model with strong friction
utilizing the Davydov D1 ansatz. It is shown that initial conditions of the
phonon bath have considerable influence on the dynamics. Counterintuitively,
even in the very strong coupling regime, quantum coherence features still
manage to survive under the polarized bath initial condition, while such
features are absent under the factorized bath initial condition. In addition, a
coherent-incoherent transition is found at a critical coupling strength alpha ~
0.1 for s=0.25 under the factorized bath initial condition. We quantify how
faithfully our ansatz follows the Schr\"{o}dinger equation, finding that the
time-dependent variational approach is robust for strong dissipation and deep
sub-Ohmic baths (s<<1).Comment: 8 pages, 6 figure
Sub-Ohmic spin-boson model with off-diagonal coupling: Ground state properties
We have carried out analytical and numerical studies of the spin-boson model
in the sub-ohmic regime with the influence of both the diagonal and
off-diagonal coupling accounted for via the Davydov D1 variational ansatz.
While a second-order phase transition is known to be exhibited by this model in
the presence of diagonal coupling only, we demonstrate the emergence of a
discontinuous first order phase transition upon incorporation of the
off-diagonal coupling. A plot of the ground state energy versus magnetization
highlights the discontinuous nature of the transition between the isotropic
(zero magnetization) state and nematic (finite magnetization) phases. We have
also calculated the entanglement entropy and a discontinuity found at a
critical coupling strength further supports the discontinuous crossover in the
spin-boson model in the presence of off-diagonal coupling. It is further
revealed via a canonical transformation approach that for the special case of
identical exponents for the spectral densities of the diagonal and the
off-diagonal coupling, there exists a continuous crossover from a single
localized phase to doubly degenerate localized phase with differing
magnetizations.Comment: 11 pages, 7 figure
Entanglement dynamics of a two-qubit system coupled individually to Ohmic baths
Developed originally for the Holstein polaron, the Davydov D1 ansatz is an
efficient, yet extremely accurate trial state for time-dependent variation of
the spin-boson model [J. Chem. Phys. 138, 084111 (2013)]. In this work, the
Dirac-Frenkel time-dependent variational procedure utilizing the Davydov D1
ansatz is implemented to study entanglement dynamics of two qubits under the
influence of two independent baths. The Ohmic spectral density is used without
the Born-Markov approximation or the rotating-wave approximation. In the strong
coupling regime finite-time disentanglement is always found to exist, while at
the intermediate coupling regime, the entanglement dynamics calculated by
Davydov D1 ansatz displays oscillatory behavior in addition to entanglement
disappearance and revival.Comment: 8 pages, 3 figure
Asymptotic Properties of Some Freud Polynomials
We study the asymptotic properties of monic orthogonal polynomials (OPs) with
respect to some Freud weights when the degree of the polynomial tends to
infinity, including the asymptotics of the recurrence coefficients, the
nontrivial leading coefficients of the monic OPs, the associated Hankel
determinants and the squares of -norm of the monic OPs. These results are
derived from the combination of the ladder operator approach, Dyson's Coulomb
fluid approach and some recent results in the literature
- …