Weak Coupling Approximation Research Articles

Wide-band tuneability, nonlinear transmission, and dynamic multistability in SQUID metamaterials

Superconducting metamaterials comprising rf SQUIDs (Superconducting QUantum Interference Devices) have been recently realized and investigated with respect to their tuneability, permeability and dynamic multistability properties. These properties are a consequence of intrinsic nonlinearities due to the sensitivity of the superconducting state to external stimuli. SQUIDs, made of a superconducting ring interrupted by a Josephson junction, possess yet another source of nonlinearity, which makes them widely tuneable with an applied dc dlux. A model SQUID metamaterial, based on electric equivalent circuits, is used in the weak coupling approximation to demonstrate the dc flux tuneability, dynamic multistability, and nonlinear transmission in SQUID metamaterials comprising non-hysteretic SQUIDs. The model equations reproduce the experimentally observed tuneability patterns, and predict tuneability with the power of an applied ac magnetic magnetic field. Moreover, the results indicate the opening of nonlinear frequency bands for energy transmission through SQUID metamaterials, for sufficiently strong ac fields.

Attenuation of excitation decay rate due to collective effect

We study a series of N oscillators, each coupled to its nearest neighbors, and linearly to a phonon field through the oscillator's number operator. We show that the Hamiltonian of a pair of adjacent oscillators, or a dimer, within the series of oscillators can be transformed into a form in which they are collectively coupled to the phonon field as a composite unit. In the weak coupling and rotating-wave approximation, the system behaves effectively as the trilinear boson model in the one excitation subspace of the dimer subsystem. The reduced dynamics of the one excitation subspace of the dimer subsystem coupled weakly to a phonon bath is similar to that of a two-level system, with a metastable state against the vacuum. The decay constant of the subsystem is proportional to the dephasing rate of the individual oscillator in a phonon bath, attenuated by a factor that depends on site asymmetry, intersite coupling, and the resonance frequency between the transformed oscillator modes, or excitons. As a result of the collective effect, the excitation relaxation lifetime is prolonged over the dephasing lifetime of an individual oscillator coupled to the same bath.

Chimera states: the existence criteria revisited.

Chimera states, representing a spontaneous breakup of a population of identical oscillators that are identically coupled, into subpopulations displaying synchronized and desynchronized behavior, have traditionally been found to exist in weakly coupled systems and with some form of nonlocal coupling between the oscillators. Here we show that neither the weak-coupling approximation nor nonlocal coupling are essential conditions for their existence. We obtain, for the first time, amplitude-mediated chimera states in a system of globally coupled complex Ginzburg-Landau oscillators. We delineate the dynamical origins for the formation of such states from a bifurcation analysis of a reduced model equation and also discuss the practical implications of our discovery of this broader class of chimera states.

Quasirelativistic Langevin equation

We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.

Dynamical paths and universality in continuous-variable open systems

We address the dynamics of quantum correlations in continuous variable open systems and analyze the evolution of bipartite Gaussian states in independent noisy channels. In particular, upon introducing the notion of dynamical path through a suitable parametrization for symmetric states, we focus attention on phenomena that are common to Markovian and non-Markovian Gaussian maps under the assumptions of weak coupling and secular approximation. We found that the dynamical paths in the parameter space are universal, that is they do depend only on the initial state and on the effective temperature of the environment, with non Markovianity that manifests itself in the velocity of running over a given path. This phenomenon allows one to map non-Markovian processes onto Markovian ones and it may reduce the number of parameters needed to study a dynamical process, e.g. it may be exploited to build constants of motions valid for both Markovian and non-Markovian maps. Universality is also observed in the value of Gaussian discord at the separability threshold, which itself is a function of the sole initial conditions in the limit of high temperature. We also prove the existence of excluded regions in the parameter space, i.e. of sets of states which cannot be linked by any Gaussian dynamical map.

Frequency-domain formulation of signal propagation in multistrip Resistive Plate Chambers and its low-loss, weak-coupling analytical approximation

In this study the signal propagation in multistrip Resistive Plate Chambers is formulated exactly in the framework of the multiconductor transmission line theory in the frequency domain, allowing losses to be incorporated. For the case of weak-coupling and low-losses a first-order expansion yields simple, fully analytical, expressions that include reflections. In this approximation the modal spectrum can be calculated analytically as well, allowing to estimate easily the strength of the modal dispersion phenomenon.

Optimization of plasmon–plasmon coupling in photorefractive layered media

In this paper we study grating-induced plasmon–plasmon coupling in photorefractive layered media using a weak-coupling approximation. The method used is applicable to general layered structures that support both plasmonic and optical modes, such as photorefractive liquid crystal cells. The approximate equations are accurate when compared to S matrix approaches and capture the plasmon propagation at the surface of the device along with the optical modes guided by the layered geometry underneath. Analysis of the resulting model provides insight into the effect of the control parameters in this device and the means to optimize the diffraction efficiency. For example, by considering the case in which the plasmon is spectrally separated from the guided modes it is possible to determine the optimum gold thickness and grating strength required to obtain the strongest possible diffraction.

A multi-site variational master equation approach to dissipative energy transfer

Unitary transformations can allow one to study open quantum systems in situations for which standard, weak-coupling type approximations are not valid. We develop here an extension of the variational (polaron) transformation approach to open system dynamics, which applies to arbitrarily large exciton transport networks with local environments. After deriving a time-local master equation in the transformed frame, we go on to compare the population dynamics predicted using our technique with other established master equations. The variational frame dynamics are found to agree with both weak coupling and full polaron master equations in their respective regions of validity. In parameter regimes considered difficult for these methods, the dynamics predicted by our technique are found to interpolate between the two. The variational method thus gives insight, across a broad range of parameters, into the competition between coherent and incoherent processes in determining the dynamical behaviour of energy transfer networks.

Three-point correlators of twist-2 operators in N=4 SYM at Born approximation

Abstract We calculate two different types of 3-point correlators involving twist-2 operators in the leading weak coupling approximation and all orders in N c in N=4 SYM theory. Each of three operators in the first correlator can be any component of twist-2 supermultiplet, though the explicit calculation was done for a particular component which is an SU(4) singlet. It is calculated in the leading, Born approximation for arbitrary spins j 1 , j 2 , j 3. The result significantly simplifies when at least one of the spins is large or equal to zero and the coordinates are restricted to the 2d plane spanned by two light-rays. The second correlator involves two twist-2 operators Tr(X∇ j1 X) + . . ., Tr(Z∇ j2 Z) + . . . and one Konishi operator $ \mathrm{Tr}{{\left[ {\overline{Z},\overline{X}} \right]}^2} $ . It vanishes in the lowest g 0 order and is computed at the leading g 2 approximation.

Dynamic control of quantum geometric heat flux in a nonequilibrium spin-boson model

We study the quantum geometric heat flux in the nonequilibrium spin-boson model. By adopting the noninteracting-blip approximation that is able to accommodate the strong system-bath coupling, we show that there exists a nonzero geometric heat flux only when the two-level system is nondegenerate. Moreover, the pumping, no pumping, and dynamic control of geometric heat flux are discussed in detail, compared to the results with Redfield weak-coupling approximation. In particular, the geometric energy transfer induced by modulation of two system-bath couplings is identified, which is exclusive to quantum transport in the strong system-bath coupling regime.

Frame Transformation Relations and Symmetry Analysis of Fluxional Symmetric Rotor Dimers

The theory of Frame transformation relations between the states of Born Oppenheimer and the weak coupling approximations is developed for polyatomic molecules. The symmetry relations are a generalization of the frame transformation relations derived by Harter and Crogman for coupled rotor molecules. A key internal symmetry label (named “soul”) is defined so that it remains a constant label for frame transformation relations, and is conserved during vibronic transitions, ionization, and even dissociation provided the nuclear spin-rotation interaction is relatively small. Simplified procedures are given for obtaining selection rules, statistical weights, and matrix elements of multipole operators for common molecules having various point symmetries.

Two-dimensional Fröhlich polaron with Rashba and Dresselhaus spin-orbit coupling

We investigate the simultaneous effect of Rashba and Dresselhaus spin-orbit interactions on the formation of Frohlich polarons in two-dimensional semiconductors in weak electron-phonon coupling approximation. The results illustrate that the spin-orbit coupling terms may significantly affect the polaron properties. We show that in the presence of both SO coupling terms the self-energy correction of the electron energy as well as the polaron effective mass exhibit an angular anisotropy unlike the case when only one of the spin-orbit coupling terms (Rashba or Dresselhaus) is considered. The simultaneous consideration of the Rashba and Dresselhaus mechanisms shows that polaronic effect may become either stronger or weaker depending on directions, a phenomenon which does not occur when the spin-orbit interaction is not taken into account.

Vacuum structure and string tension in Yang-Mills dimeron ensembles

We numerically simulate ensembles of SU(2) Yang-Mills dimeron solutions with a statistical weight determined by the classical action and perform a comprehensive analysis of their properties as a function of the bare coupling. In particular, we examine the extent to which these ensembles and their classical gauge interactions capture topological and confinement properties of the Yang-Mills vacuum. This also allows us to put the classic picture of meron-induced quark confinement, with the confinement-deconfinement transition triggered by dimeron dissociation, to stringent tests. In the first part of our analysis we study spacial, topological-charge and color correlations at the level of both the dimerons and their meron constituents. At small to moderate couplings, the dependence of the interactions between the dimerons on their relative color orientations is found to generate a strong attraction (repulsion) between nearest neighbors of opposite (equal) topological charge. Hence, the emerging short- to mid-range order in the gauge-field configurations screens topological charges. With increasing coupling this order weakens rapidly, however, in part because the dimerons gradually dissociate into their less localized meron constituents. Monitoring confinement properties by evaluating Wilson-loop expectation values, we find the growing disorder due to the long-range tails of these progressively liberated merons to generate a finite and (with the coupling) increasing string tension. The short-distance behavior of the static quark-antiquark potential, on the other hand, is dominated by small, ``instantonlike'' dimerons. String tension, action density and topological susceptibility of the dimeron ensembles in the physical coupling region turn out to be of the order of standard values. Hence, the above results demonstrate without reliance on weak-coupling or low-density approximations that the dissociating dimeron component in the Yang-Mills vacuum can indeed produce a meron-populated confining phase. The density of coexisting, hardly dissociated and thus instantonlike dimerons seems to remain large enough, on the other hand, to reproduce much of the additional phenomenology successfully accounted for by nonconfining instanton vacuum models. Hence, dimeron ensembles should provide an efficient basis for a more complete description of the Yang-Mills vacuum.

Energy exchange, localization, and transfer in nanoscale systems (weak-coupling approximation)

It is shown that both an adequate understanding and effective analysis of energy exchange, localization, and transfer in nanoscale systems is closely related to important aspects of the “wave-particle” duality, one of the key concepts of quantum mechanics. Due to the revealed similarities between the mathematical description of weakly coupled classical oscillators and multilevel quantum systems, this relation turns out to be essential for classical physics as well. Although the development of quantum field theory led, in fact, to the abolition of the wave-particle duality at the fundamental level, putting into the forefront the oscillatory field in the vacuum and imparting to quantized particles the status of field excitations, the wave-particle dilemma continues to be a powerful heuristic principle of theoretical analysis in quantum and classical physics. Within the framework of this approach, it is possible to identify two limiting cases that allow a natural interpretation as applied to polymer physics. In the continuum approximation, very long macromolecules in polymer crystals and other ordered polymer systems (e.g., in the DNA double helix), although considerably more complex in structure than spatially one-dimensional models of nonlinear physics, are ideal objects for the application of ideas and methods of classical nonlinear field theory,. Depending on the conditions of operation, these systems feature both wavelike (normal vibrations and waves) and solitonlike (particlelike) excitation of the nonlinear field, or some combination thereof. The main difficulties to be overcome here are associated with an asymptotic reduction of realistic models of polymer chains and crystals to analytically solvable models. However, for oligomers, with relatively short chains, and nanostructures (second limiting case), it became necessary to develop a fundamentally new approach, since in this case, the formation of localized nonlinear excitations and irreversible energy transfer are preceded (in the level of excitation) by the stage of intense energy exchange between certain groups of particles, referred to as effective particles. Most intense energy transfer is described in terms of limiting phase trajectories, a notion alternative to classical nonlinear normal modes and quantum stationary states. The possibility of introducing effective particles becomes apparent when the initial molecular chain is reduced (in a certain range of its frequencies) to a system of weakly coupled nonlinear oscillators, which is described by the same equations as the multilevel quantum system. With increasing excitation energy, a threshold is reached at which intense energy transfer gives way to the localization of energy on the initially excited effective particle or to its transfer along the chain. In view of the quantum-classical analogy, the analysis of classical linear and nonlinear oscillator models of nanoscale systems is applicable to multilevel quantum systems. In both cases, the asymptotic nature of the wave-particle duality manifests itself, which makes it possible to clarify the relationship between the existing interpretations of it.

Steady-state thermal transport in anharmonic systems: Application to molecular junctions

We develop a general theory for thermal transport in anharmonic systems under the weak system-bath coupling approximation similar to the quantum master equation formalism. A current operator is derived, which is valid not only in the steady state, but in the transient regime as well. Here we focus on the effects of anharmonicity on the steady-state thermal conductance of a mono and diatomic molecular junctions. We also study molecules being confined in a double-well potential. We find that when the molecules have a non-linear on-site potential the low-temperature thermal conductance is dramatically affected by the strength of non-linearity, whereas for the diatomic molecule connected by an anharmonic spring the strength of anharmonicity plays almost no role in the low-temperature regime. In case of the molecules confined in a double-well potential we find that the height of the barrier greatly affects the thermal conductance; once the molecules can feel the effect of the barrier we observe negative differential thermal conductance at both high and low temperatures.

Classical master equation for excitonic transport under the influence of an environment

In a previous paper [Phys. Rev. E 83, 051911 (2011)] we have shown that the results of a quantum-mechanical calculation of electronic energy transfer (EET) over aggregates of coupled monomers can be described also by a model of interacting classical electric dipoles in a weak-coupling approximation, which we referred to as the realistic coupling approximation (RCA). The method was illustrated by EET on a simple linear chain of molecules and also by energy transfer on an arrangement of monomers corresponding to that of the Fenna-Matthews-Olson (FMO) complex relevant for photosynthesis. The study was limited to electronic degrees of freedom, since this is the origin of coherent EET in the quantum case. Nevertheless, more realistic models of EET require the inclusion of the decohering effects of coupling to an environment, when the molecular aggregate becomes an open quantum system. Here we consider the quantum description of EET on a linear chain and on the FMO complex, incorporating environment coupling and constructing the classical version of the same systems in the density matrix formalism. The close agreement of the exact quantum and exact classical results in the RCA is demonstrated and justified analytically in the RCA. This lends further support to the conclusion that the coherence properties of EET in the FMO complex are evident at the classical level and should not be ascribed as solely due to quantum effects.

Kinetic theory of spatially homogeneous systems with long-range interactions: I. General results

We review and complete the literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the Lenard-Balescu equation which is valid in a weak coupling approximation. When collective effects are neglected it reduces to the Landau equation and when collisions (correlations) are neglected it reduces to the Vlasov equation. The relaxation of a test particle in a bath is described by a Fokker-Planck equation involving a diffusion term and a friction term. For a thermal bath, the diffusion and friction coefficients are connected by an Einstein relation. General expressions of the diffusion and friction coefficients are given, depending on the potential of interaction and on the dimension of space. We also discuss the scaling with N (number of particles) or with Λ (plasma parameter) of the relaxation time towards statistical equilibrium. Finally, we consider the effect of an external stochastic forcing on the evolution of the system and compute the corresponding term in the kinetic equation.

Repulsive long-range forces between anisotropic atoms and dielectrics

We investigate long-range forces between atoms with anisotropic electric polarizability interacting with dielectrics having anisotropic permittivity in the weak-coupling approximation. Unstable configurations in which the force between the objects is repulsive are constructed. Such configurations exist for three anisotropic atoms as well as for an anisotropic atom above a dielectric plate with a hole whose permittivity is anisotropic. Apart from the absolute magnitude of the force, the dependence on the configuration is qualitatively the same as for metallic objects for which the anisotropy is a purely geometric effect. In the weak limit closed analytic expressions for rather complicated configurations are obtained. The non-monotonic dependence of the interaction energy on separation is related to the fact that the electromagnetic Green's dyadic is not positive definite. The analysis in the weak limit is found to also semi-quantitatively explain the dependence of Casimir forces on the orientation of anisotropic dielectrics observed experimentally. Contrary to the scalar case, irreducible electromagnetic three-body energies can change sign. We trace this to the fact that the electromagnetic Green's dyadic is not positive definite.

Quasi non-Markovian Approach to the Study of Decoherence of a Controlled-Not Quantum Gate in a Chain of Few Nuclear Spins Quantum Computer

We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperature which is unlikely to be measured, and at high dissipation there is a difference which is likely to be measured at any temperature.

Effect of a gap on the decoherence of a qubit

We revisit the problem of the decoherence and relaxation of a central spin coupled to a bath of conduction electrons. We consider both metallic and semiconducting baths to study the effect of a gap in the bath density of states (DOS) on the time evolution of the density matrix of the central spin. We use two weak coupling approximation schemes to study the decoherence. At low temperatures, though the temperature dependence of the decoherence rate in the case of a metallic bath is the same irrespective of the details of the bath, the same is not true for the semiconducting bath. We also calculate the relaxation and decoherence rates as a function of external magnetic fields applied both on the central spin and the bath. We find that in the presence of the gap, there exists a certain regime of fields, for which surprisingly, the metallic bath has lower rates of relaxation and decoherence than the semiconducting bath.