In What Sense are Psychical States Extended?

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Nonlinear response theory for Markov processes: Simple models for glassy relaxation

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature $T_0$ determined by the value of the asymmetry. In a narrow temperature range around $T_0$, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both, low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than $T_0$), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables is considered that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.Comment: 23 pages, 10 figure

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, $D_{ab}=| \Phi_a > < \Phi_b |$, where each state evolves according to the Stochastic Schr\"odinger Equation (SSE) given in ref. \cite{Jul02}. A stochastic Liouville-von Neumann equation is derived as well as the associated Bogolyubov-Born-Green-Kirwood-Yvon (BBGKY) hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended Time-Dependent Hartree-Fock (Extended TDHF) scheme. In this stochastic mean field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.Comment: 12 pages, 1 figur

Dissipation in a rotating frame: master equation, effective temperature and Lamb-shift

Motivated by recent realizations of microwave-driven nonlinear resonators in superconducting circuits, the impact of environmental degrees of freedom is analyzed as seen from a rotating frame. A system plus reservoir model is applied to consistently derive in the weak coupling limit the master equation for the reduced density in the moving frame and near the first bifurcation threshold. It turns out that additional interactions between momenta of system and bath appear which have been omitted in previous studies. Explicit expressions for the effective temperature and the Lamb-shift are given which for ohmic baths are in agreement with experimental findings, while for structured environments population inversion is predicted that may qualitatively explain recent observations.Comment: 7 pages, 5 figure

Fragmentation dynamics of the ethyl bromide and ethyl iodide cations: a velocity-map imaging study

The photodissociation dynamics of ethyl bromide and ethyl iodide cations (C2H5Br+ and C2H5I+) have been studied. Ethyl halide cations were formed through vacuum ultraviolet (VUV) photoionization of the respective neutral parent molecules at 118.2 nm, and were photolysed at a number of ultraviolet (UV) photolysis wavelengths, including 355 nm and wavelengths in the range from 236 to 266 nm. Time-of-flight mass spectra and velocity-map images have been acquired for all fragment ions and for ground (Br) and spin–orbit excited (Br*) bromine atom products, allowing multiple fragmentation pathways to be investigated. The experimental studies are complemented by spin–orbit resolved ab initio calculations of cuts through the potential energy surfaces (along the RC–Br/I stretch coordinate) for the ground and first few excited states of the respective cations. Analysis of the velocity-map images indicates that photoexcited C2H5Br+ cations undergo prompt C–Br bond fission to form predominantly C2H5+ + Br* products with a near-limiting ‘parallel’ recoil velocity distribution. The observed C2H3+ + H2 + Br product channel is thought to arise via unimolecular decay of highly internally excited C2H5+ products formed following radiationless transfer from the initial excited state populated by photon absorption. Broadly similar behaviour is observed in the case of C2H5I+, along with an additional energetically accessible C–I bond fission channel to form C2H5 + I+ products. HX (X = Br, I) elimination from the highly internally excited C2H5X+ cation is deemed the most probable route to forming the C2H4+ fragment ions observed from both cations. Finally, both ethyl halide cations also show evidence of a minor C–C bond fission process to form CH2X+ + CH3 products

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behaviour of a simple homogeneous Bose gas.Comment: Replaced paper same as original; correction to author list on cond-mat mad

Unraveling quantum dissipation in the frequency domain

We present a quantum Monte Carlo method for solving the evolution of an open quantum system. In our approach, the density operator evolution is unraveled in the frequency domain. Significant advantages of this approach arise when the frequency of each dissipative event conveys information about the state of the system.Comment: 4 pages, 4 Postscript figures, uses RevTe

Stimulated Raman adiabatic passage in an open quantum system: Master equation approach

A master equation approach to the study of environmental effects in the adiabatic population transfer in three-state systems is presented. A systematic comparison with the non-Hermitian Hamiltonian approach [N. V. Vitanov and S. Stenholm, Phys. Rev. A {\bf 56}, 1463 (1997)] shows that in the weak coupling limit the two treatments lead to essentially the same results. Instead, in the strong damping limit the predictions are quite different: in particular the counterintuitive sequences in the STIRAP scheme turn out to be much more efficient than expected before. This point is explained in terms of quantum Zeno dynamics.Comment: 11 pages, 4 figure

Heisenberg picture operators in the quantum state diffusion model

A stochastic simulation algorithm for the computation of multitime correlation functions which is based on the quantum state diffusion model of open systems is developed. The crucial point of the proposed scheme is a suitable extension of the quantum master equation to a doubled Hilbert space which is then unraveled by a stochastic differential equation.Comment: LaTeX2E, 6 pages, 3 figures, uses iopar

Exact stochastic simulation of dissipation and non-Markovian effects in open quantum systems

The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic and non-local in time and where the standard two-times correlation functions of the environment appear naturally. Since no approximation is made, the presented theory incorporates exactly dissipative and non-Markovian effects. Applications to the spin-boson model coupled to a heat-bath with various coupling regimes and temperature show that the presented stochastic theory can be a valuable tool to simulate exactly the dynamics of open quantum systems. Links with stochastic Schroedinger equation method and possible extensions to "imaginary time" propagation are discussed.Comment: accepted for publication in Physical Review