Energy-transfer and quantum trajectories in quasi-molecular networks

Continuous measurement models are conveniently based on master equations specified by the respective Hamiltonian and appropriate environment operators. As demonstrated by stochastic unraveling, the latter specify the dynamical process rather than static detection modes. We show that certain environment operators acting on a simple system may, in fact, require extended networks for implementation: Their Hamilton parameters re-appear in the effective environment operators of the reduced model. The resulting quantum trajectories typically involve competing paths, which may give rise to different fluctuation and noise properties even when the corresponding ensemble behavior is practically the same. Received: 21 July 1997 / Received in final form: 10 November 1997 / Accepted: 27 October 1997     

Cavitation in superfluid helium-4 at low temperature

We have studied the nucleation of bubbles in pure superfluid helium-4 at temperatures down to 65 mK. We have found that the nucleation is a stochastic process, and that at temperatures below 600 mK the nucleation rate is independent of temperature. These results are consistent with the assumption that the nucleation takes place via quantum tunneling. Received: 15 November 1997 / Received in final form: 19 December 1997 / Accepted: 22 January 1998     

Boundary condition histograms for modulated phases

Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical properties: it combines fluctuating boundary conditions and specific histogram techniques. Our approach concerns classical systems possessing a continuous symmetry as well as quantum systems. In particular, current-current correlation functions, which probe large scale coherence of the states, can be accurately evaluated. We illustrate our method on a frustrated two dimensional XY model. Received: 9 September 1997 / Revised: 17 October 1997 / Accepted: 3 November 1997     

Noise-assisted mound coarsening in epitaxial growth

Two types of mechanisms are proposed for mound coarsening during unstable epitaxial growth: stochastic, due to deposition noise, and deterministic, due to mass currents driven by surface energy differences. Both yield the relation H=(RWL)² between the typical mound height W, mound size L, and the film thickness H. An analysis of simulations and experimental data shows that the parameter R saturates to a value which discriminates sharply between stochastic () and deterministic () coarsening. We derive a scaling relation between the coarsening exponent 1/z and the mound-height exponent which, for a saturated mound slope, yields . Received: 11 November 1997 / Revised in final form: 28 November 1997 / Accepted: 28 November 1997     

A Kinetic Theory Approach to Quantum Gravity

We describe a kinetic theory approach to quantum gravity by which we mean a theory of the microscopic structure of space-time, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotty poles: quantum matter field on the right and space-time on the left. Each rung connecting the corresponding knots represents a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein–Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: (1) deduce the correlations of metric fluctuations from correlation noise in the matter field; (2) reconstituting quantum coherence—this is the reverse of decoherence—from these correlation functions; and (3) use the Boltzmann–Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding space-time counterparts. This will give us a hierarchy of generalized stochastic equations—call them the Boltzmann–Einstein hierarchy of quantum gravity—for each level of space-time structure, from the the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).     

Exact two-loop vacuum polarization correction to the Lamb shift in hydrogenlike ions

We present a calculation scheme for the two-loop vacuum polarization correction of order to the Lamb shift of hydrogenlike high-Z atoms. The interaction with the external Coulomb field is taken into account to all orders in . By means of a modified potential approach the problem is reduced to the evaluation of effective one-loop vacuum polarization potentials. An expression for the energy shift is deduced within the framework of partial wave decomposition performing appropriate subtractions. Exact results for the two-loop vacuum polarization contribution to the Lamb shift of K- and L-shell electron states in hydrogenlike Lead and Uranium are presented. Received: 10 August 1997 / Revised: 31 October 1997 / Accepted: 18 November 1997     

Stability of Semiclassical Gravity Solutions with Respect to Quantum Metric Fluctuations

We discuss the stability of semiclassical gravity solutions with respect to small quantum corrections by considering the quantum fluctuations of the metric perturbations around the semiclassical solution. We call the attention to the role played by the symmetrized 2-point quantum correlation function for the metric perturbations, which can be naturally decomposed into two separate contributions: intrinsic and induced fluctuations. We show that traditional criteria on the stability of semiclassical gravity are incomplete because these criteria based on the linearized semiclassical Einstein equation can only provide information on the expectation value and the intrinsic fluctuations of the metric perturbations. By contrast, the framework of stochastic semiclassical gravity provides a more complete and accurate criterion because it contains information on the induced fluctuations as well. The Einstein–Langevin equation therein contains a stochastic source characterized by the noise kernel (the symmetrized 2-point quantum correlation function of the stress tensor operator) and yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. These points are illustrated with the example of Minkowski space-time as a solution to the semiclassical Einstein equation, which is found to be stable under both intrinsic and induced fluctuations.     

Master equations for time correlation functions of a quantum system interacting with stochastic perturbations and applications to emission and absorption line shapes

The stochastic and quantum dynamics of open quantum systems interacting with stochastic perturbations in considered. The master equations for one time and multi-time correlation functions of such a system are derived to all orders in the interaction with the stochastic perturbations. The importance of the non-markovian character of such equations in the study of various problems in optical resonance is discussed. The simplified form of the non-markovian master equations in Born approximation is also given. It is shown that such non-markovian master equations in Born approximation are exact if there is only one random perturbation, of the telegraphic signal type, acting on the system. The master equations for the linear response functions of an open system interacting with stochastic perturbations are also derived. The non-markovian master equations for multitime correlations are used to study the behaviour of two level atoms interacting with fluctuating laser fields. Both amplitude and phase fluctuations are taken into account. Explicit results are presented for the spectrum of resonance fluorescence, absorption spectrum, photon antibunching effects etc. The calculations are done for arbitrary values of the relaxation parameters and intial conditions. In general the fluorescence spectrum is found to be asymmetric for off resonant fields.     

Spontaneous emission of an excited two-level atom without both rotating-wave and Markovian approximation

The spontaneous emission of an excited atom is analyzed by quantum stochastic trajectory approach without both rotating-wave approximation and Markovian approximation. The atom finite size effect is also taken into account. We show by an example that the correction due to the counter-rotating wave term is rather small, even for the largest atomic number of real nuclei. Received 10 July 2002 / Received in final form 12 November 2002 Published online 4 February 2003     

单量子双能级系统和双态系统关联函数的研究

以具有简单三能级结构染料分子的单量子系统为研究对象,用带有边界条件的速率方程来反映低功率单色连续激光激励下单分子发射荧光的动力学过程.该方法可以通过时间分辨光子探测获得处理单分子动力学随机过程.研究给出了一种通过求解反映单量子系统动力学过程的物理量——延迟函数计算关联函数的方法,并给出了双能级系统和双态系统延迟函数和关联函数的具体表达式.研究表明,在实际测量中只要获得关联函数曲线,就可以通过数据拟合计算出分子跃迁的动力学参量.     

Nonlinear Schrödinger equation and superfluid hydrodynamics

We show that it is possible to generalize the Gross-Pitaevskii equation describing superfluidity in order to recover the two-fluid model, in the hydrodynamic limit, when the deviations from the equilibrium state are of long wavelength. When short distances are relevant, it is possible to keep trace of the purely quantum, non-hydrodynamic term of the Gross-Pitaevskii equation, so that the Hills-Roberts model, which describes the healing phenomenon, is finally obtained. Received: 19 August 1997 / Revised: 16 October 1997 / Accepted: 6 November 1997     

Parameter estimation for the piecewice-polynomial mean value trend of a stochastic time series

We consider the problem of mean value trend estimation for a stochastic time series in a mixture with noise. The trend is simulated as a polynomial function of time with parameters changing discontinuously at a random instant. The proposed solution of this problem is based on the optimal nonlinear filtering theory for pulsed Markovian processes. An algorithm for approximate estimation of piesewise-linear trend parameters is devised as an example. The results of numerical simulation of a synthesized algorithm are presented. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 11, pp. 1405–1415, November, 1997.     

Simulated quantum computation of global minima

Finding the optimal solution to a complex optimisation problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations N reduced from O(N) in classical simulation to O(N ^1/2) in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimisation to treat larger systems.     

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, “weak” or “strong”, interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular ,are found to be robust against these perturbations. Received: 7 October 1997 / Accepted: 19 November 1997     

Quantum Monte Carlo Study of Frustrated Spin Chain Under External Field

In this paper a stochastic series expansion quantum Monte Carlo algorithm is used to study a frustrated spin chain with diagonal next-nearest-neighbor interactions. The detailed balance conditions are carefully analyzed to improve the efficiency of simulation process. As an application of this algothrim, the total magnetization, the static structure factor and spin-stiffness arecalculated for a certain set of system parameters as a function of external field strength.     

Noise effect on Grover algorithm

The decoherence effect on Grover algorithm has been studied numerically through a noise modelled by a depolarizing channel. Two types of error are introduced characterizing the qubit time evolution and gate application, so the noise is directly related to the quantum network construction. The numerical simulation concludes an exponential damping law for the successive probability of the maxima as time increases. We have obtained an allowed-error law for the algorithm: the error threshold for the allowed noise behaves as ε_th(N) ∼1/N^1.1 (N being the size of the data set). As the power of N is almost one, we consider the Grover algorithm as robust to a certain extent against decoherence. This law also provides an absolute threshold: if the free evolution error is greater than 0.043, Grover algorithm does not work for any number of qubits affected by the present error model. The improvement in the probability of success, in the case of two qubits has been illustrated by using a fault-tolerant encoding of the initial state by means of the [[7,1,3]] quantum code.     

On the Structure of the Small Quantum Cohomology Rings of Projective Hypersurfaces

We give an explicit procedure which computes for degree d≤ 3 the correlation functions of topological sigma model (A-model) on a projective Fano hypersurface X as homogeneous polynomials of degree d in the correlation functions of degree 1 (number of lines). We extend this formalism to the case of Calabi–Yau hypersurfaces and explain how the polynomial property is preserved. Our key tool is the construction of universal recursive formulas which express the structure constants of the quantum cohomology ring of X as weighted homogeneous polynomial functions of the constants of the Fano hypersurface with the same degree and dimension one more. We propose some conjectures about the existence and the form of the recursive laws for the structure constants of rational curves of arbitrary degree. Our recursive formulas should yield the coefficients of the hypergeometric series used in the mirror calculation. Assuming the validity of the conjectures we find the recursive laws for rational curves of degree four. Received: 29 November 1996 / Accepted: 15 March 1999     

Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on p in the following way: ν(p) = νp and λ(p) = λp ^3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp ². It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models. Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: ealbano@inifta.unlp.edu.ar