Smearing Formula for Higher-Order Effective Classical Potentials

In the variational approach to quantum statistics, a smearing formula describes efficiently the consequences of quantum fluctuations upon an interaction potential. The result is an effective classical potential from which the partition function can be obtained by a simple integral. In this work, the smearing formula is extended to higher orders in the variational perturbation theory. An application to the singular Coulomb potential exhibits the same fast convergence with increasing orders that has been observed in previous variational perturbation expansions of the anharmonic oscillator with quartic potential.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re267/preprint.htm

Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory

We show that in applications of variational theory to quantum field theory it is essential to account for the correct Wegner exponent omega governing the approach to the strong-coupling, or scaling limit. Otherwise the procedure either does not converge at all or to the wrong limit. This invalidates all papers applying the so-called delta-expansion to quantum field theory.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/34

An exact equilibrium reduced density matrix formulation I: The influence of noise, disorder, and temperature on localization in excitonic systems

An exact method to compute the entire equilibrium reduced density matrix for systems characterized by a system-bath Hamiltonian is presented. The approach is based upon a stochastic unraveling of the influence functional that appears in the imaginary time path integral formalism of quantum statistical mechanics. This method is then applied to study the effects of thermal noise, static disorder, and temperature on the coherence length in excitonic systems. As representative examples of biased and unbiased systems, attention is focused on the well-characterized light harvesting complexes of FMO and LH2, respectively. Due to the bias, FMO is completely localized in the site basis at low temperatures, whereas LH2 is completely delocalized. In the latter, the presence of static disorder leads to a plateau in the coherence length at low temperature that becomes increasingly pronounced with increasing strength of the disorder. The introduction of noise, however, precludes this effect. In biased systems, it is shown that the environment may increase the coherence length, but only decrease that of unbiased systems. Finally it is emphasized that for typical values of the environmental parameters in light harvesting systems, the system and bath are entangled at equilibrium in the single excitation manifold. That is, the density matrix cannot be described as a product state as is often assumed, even at room temperature. The reduced density matrix of LH2 is shown to be in precise agreement with the steady state limit of previous exact quantum dynamics calculations.Comment: 37 pages, 12 figures. To appear in Phys. Rev.

Synchronization in a neuronal feedback loop through asymmetric temporal delays

We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical value. We show that the angular frequency of the limit cycle is independent of an asymmetry in the delays. However, the delay asymmetry determines the phase difference between the periodic activities of the two components. Specifically, when the connection with negative coupling has a delay much larger than the delay for the positive coupling, the system approaches in-phase synchrony between the two components. Employing variational perturbation theory (VPT), we achieve an approximate analytical evaluation of the phase shift, in good agreement with numerical results.Comment: 5 pages, 4 figure

A path integral approach to the dynamics of a random chain with rigid constraints

In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimensions has been limited to two. The problem of describing the fluctuations of the chain in the limit in which it becomes a continuous system is solved using a path integral approach, in which the constraints are imposed with the insertion in the path integral of suitable Dirac delta functions. It is shown that the probability distribution of the possible conformations in which the fluctuating chain can be found during its evolution in time coincides with the partition function of a field theory which is a generalization of the nonlinear sigma model in two dimensions. Both the probability distribution and the generating functional of the correlation functions of the positions of the beads are computed explicitly in a semiclassical approximation for a ring-shaped chain.Comment: 36 pages, 2 figures, LaTeX + REVTeX4 + graphicx, minor changes in the text, reference adde

Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach

A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields. An exact hierarchical equations of motion formalism is constructed on the basis of calculus-on-path-integral algorithm, via the auxiliary influence generating functionals related to the interaction bath correlation functions in a parametrization expansion form. The corresponding continued-fraction Green's functions formalism for quantum dissipation is also presented. Proposed further is the principle of residue correction, not just for truncating the infinite hierarchy, but also for incorporating the small residue dissipation that may arise from the practical difference between the true and the parametrized bath correlation functions. The final residue-corrected hierarchical equations of motion can therefore be used practically for the evaluation of arbitrary dissipative quantum systems.Comment: 12 pages, submitted to PR

Renormalized thermodynamics from the 2PI effective action

High-temperature resummed perturbation theory is plagued by poor convergence properties. The problem appears for theories with bosonic field content such as QCD, QED or scalar theories. We calculate the pressure as well as other thermodynamic quantities at high temperature for a scalar one-component field theory, solving a three-loop 2PI effective action numerically without further approximations. We present a detailed comparison with the two-loop approximation. One observes a strongly improved convergence behavior as compared to perturbative approaches. The renormalization employed in this work extends previous prescriptions, and is sufficient to determine all counterterms required for the theory in the symmetric as well as the spontaneously broken phase.Comment: 20 pages, 7 figures; PRD version, references added, very minor change

Bilayer Membrane in Confined Geometry: Interlayer Slide and Steric Repulsion

We derived free energy functional of a bilayer lipid membrane from the first principles of elasticity theory. The model explicitly includes position-dependent mutual slide of monolayers and bending deformation. Our free energy functional of liquid-crystalline membrane allows for incompressibility of the membrane and vanishing of the in-plane shear modulus and obeys reflectional and rotational symmetries of the flat bilayer. Interlayer slide at the mid-plane of the membrane results in local difference of surface densities of the monolayers. The slide amplitude directly enters free energy via the strain tensor. For small bending deformations the ratio between bending modulus and area compression coefficient, Kb/KA, is proportional to the square of monolayer thickness, h. Using the functional we performed self-consistent calculation of steric potential acting on bilayer between parallel confining walls separated by distance 2d. We found that temperature-dependent curvature at the minimum of confining potential is enhanced four times for a bilayer with slide as compared with a unit bilayer. We also calculate viscous modes of bilayer membrane between confining walls. Pure bending of the membrane is investigated, which is decoupled from area dilation at small amplitudes. Three sources of viscous dissipation are considered: water and membrane viscosities and interlayer drag. Dispersion has two branches. Confinement between the walls modifies the bending mode with respect to membrane in bulk solution. Simultaneously, inter-layer slipping mode, damped by viscous drag, remains unchanged by confinement.Comment: 23 pages,3 figures, pd

Effects of tunnelling and asymmetry for system-bath models of electron transfer

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.Comment: 10 pages, 3 figure

Exact quantum dissipative dynamics under external time-dependent fields driving

Exact and nonperturbative quantum master equation can be constructed via the calculus on path integral. It results in hierarchical equations of motion for the reduced density operator. Involved are also a set of well--defined auxiliary density operators that resolve not just system--bath coupling strength but also memory. In this work, we scale these auxiliary operators individually to achieve a uniform error tolerance, as set by the reduced density operator. An efficient propagator is then proposed to the hierarchical Liouville--space dynamics of quantum dissipation. Numerically exact studies are carried out on the dephasing effect on population transfer in the simple stimulated Raman adiabatic passage scheme. We also make assessments on several perturbative theories for their applicabilities in the present system of study