Continuum Of Modes Research Articles

Numerical Renormalization Group at Marginal Spectral Density: Application to Tunneling in Luttinger Liquids

Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a numerical renormalization group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a nonperturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single static defect.

Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion

We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed.

Geodesic acoustic modes and zonal flows in rotating large-aspect-ratio tokamak plasmas

The effect of equilibrium plasma rotation (toroidal and poloidal) on low-frequency, electrostatic modes—the geodesic acoustic modes (GAMs) and the zonal flows (ZFs)—in large aspect ratio tokamaks is studied within the framework of ideal MHD. It is shown that the plasma rotation results in a frequency up-shift of the ordinary GAM. The new branch of continuum modes induced by the poloidal rotation is found. This mode originates from the opposite sign Doppler shift of frequency due to poloidal rotation for m = ±1 poloidal side-band harmonics of the perturbed mass density, pressure and parallel velocity. In the case of slow poloidal rotation (ΩP ≪ cs/qR0) its frequency is close to the sound frequency cs/qR0 (ΩP is the poloidal angular velocity, cs is the speed of sound, q is the safety factor and R0 is the major radius of tokamak). The mode can be called the rotation-induced acoustic mode. This mode disappears in the case of purely toroidal plasma rotation. The frequency of the new mode in the case of relatively slow poloidal rotation (ΩP ⩽ cs/qR0) is lower than the frequency of the ordinary GAM modified by plasma rotation. In the case of larger poloidal angular velocities ΩP (ΩP ⩾ 2cs/qR0) the mode becomes unstable and is identified as the unstable ZF. With a further increase in the poloidal angular velocity at constant toroidal angular velocity the instability is suppressed, and the mode turns again into a marginally stable, oscillating mode.

Generation of entanglement density within a reservoir

We study a single two-level atom interacting with a reservoir of modes defined by its reservoir structure function. Within this framework we are able to define a density of entanglement involving a continuum of reservoir modes. The density of entanglement is derived for a system with a single excitation by taking a limit of the global entanglement. Utilizing the density of entanglement we quantify the entanglement between the atom and the modes, and also between the reservoir modes themselves.

Mechanics of V-shaped conjugate strike-slip faults and the corresponding continuum mode of continental deformation

V-shaped conjugate strike-slip faults occur widely on Earth, Venus, and Mars in the solar system. They commonly lie at 60°–75° in map view from the maximum compressive stress (σ 1 ) direction. This fault pattern cannot be explained directly by the Coulomb fracture criterion, which predicts the formation of X-shaped shear fractures at 30° from the σ 1 direction. Possible explanations of this odd fault geometry include rotation of early formed Coulomb fractures or reactivation of preexisting weakness. Here, we show that none of these mechanisms is feasible for the formation of a late Cenozoic conjugate strike-slip fault system in central Tibet. Instead, its initiation can be best explained by distributed deformation during the formation of two parallel and adjoining shear zones that have opposing senses of shear. Our suggestion is based on the current global positioning system (GPS) velocity field in Tibet, which can be divided into two east-trending shear zones: a northern left-slip zone consisting of active ENE-striking left-slip faults, and a southern right-slip zone consisting of active WNW-striking right-slip faults. The correlation between the GPS strain field and the fault pattern suggests that the central Tibet conjugate faults may have initiated as two sets of Riedel shears in the two parallel but separate shear zones. Because the two east-trending shear zones also experience north-south contraction, we refer to this mechanism of conjugate-fault formation as paired general-shear (PGS) deformation. Assuming a Newtonian fluid, the observed Tibetan GPS velocity field requires the paired shear zones to have formed either by gravitational spreading of the Tibetan lithosphere or a horizontal shear at the base of the upper crust or mantle lithosphere. We demonstrate the feasibility of the two inferred mechanisms for the formation of V-shaped conjugate faults using simple sandbox experiments. Our paired general-shear (PGS) model implies that the combined effect of the state of strain and the state of stress favors only one set (i.e., Riedel shear) of Coulomb conjugate shear fractures under general shear flow. It also requires continuum deformation rather than discrete extrusion tectonics as the most dominant mode of deformation during the late Cenozoic development of the central Tibetan Plateau.

Entanglement dynamics of two independent cavity-embedded quantum dots

We investigate the dynamical behavior of entanglement in a system made of two solid-state emitters, as two quantum dots, embedded in two separated microcavities. In these solid-state systems, in addition to the coupling with the cavity mode, the emitter is coupled to a continuum of leaky modes providing additional losses and is also subjected to a phonon-induced pure dephasing mechanism. We model this physical configuration as a multipartite system composed of two independent parts each containing a qubit embedded in a single-mode cavity, exposed to cavity losses, spontaneous emission and pure dephasing. We study the time evolution of entanglement of this multipartite open system, finally applying this theoretical framework to the case of currently available solid-state quantum dots in microcavities.

Anomalous strong exchange narrowing in excitonic systems

We investigate theoretically the phenomenon of exchange narrowing in the absorption spectrum of a chain of monomers, which are coupled via resonant dipole-dipole interaction. The individual (uncoupled) monomers exhibit a broad absorption line shape due to the coupling to an environment consisting of a continuum of vibrational modes. Upon increasing the interaction between the monomers, the absorption spectrum of the chain narrows. For a non-Markovian environment with a Lorentzian spectral density, we find a narrowing of the peak width [full width at half maximum (FWHM)] by a factor 1∕N, where N is the number of monomers. This is much stronger than the usual 1/√N narrowing. Furthermore, it turns out that for a Markovian environment no exchange narrowing at all occurs. The relation of different measures of the width (FWHM, standard deviation) is discussed.

The stability of a terahertz receiver based on a superconducting integrated receiver

We present the results of stability testing of a terahertz radiometer based on asuperconducting receiver with a SIS tunnel junction as the mixer and a flux-flowoscillator as the local oscillator. In the continuum mode, the receiver with a noisetemperature of 95 K at 510 GHz measured over the intermediate frequency(IF) passband of 4–8 GHz offered a noise equivalent temperature difference of10 ± 1 mK at an integration time of 1 s. We offer a method to significantly increase the integrationtime without the use of complex measurement equipment. The receiver observed a strongsignal over a final detection bandwidth of 4 GHz and offered an Allan time of 5 s.

Far‐ and Mid‐Infrared Spectroscopic Analysis of the Substrate‐Induced Structural Dynamics of Respiratory Complex I

The catalytic activity of the respiratory NADH:ubiquinone oxidoreductase (complex I) is based on conformational reorganizations. Herein we probe the effect of substrates on the conformational flexibility of complex I by means of (1)H/(2)H exchange kinetics at the level of the amide proton in the mid-infrared spectral range (1700-1500 cm(-1)). Slow, medium, and fast exchanging domains are distinguished that reveal different accessibilities to the solvent. Whereas amide hydrogens undergo rapid exchange with the solvent in an open structure, hydrogens experience much slower exchange when they are involved in H-bonded structures or when they are sterically inaccessible for the solvent. The results indicate a structure that is more open in the presence of both NADH and quinon. Complementary information on the overall internal hydrogen bonding of the protein was probed in the far infrared (300-30 cm(-1)), a spectral range that includes a continuum mode of the hydrogen bonding signature.

Casimir effect of massive vector fields

We study the Casimir effect due to a massive vector field in a system of two parallel plates made of real materials, in an arbitrary magnetodielectric background. The plane waves satisfying the Proca equations are classified into transverse modes and longitudinal modes which have different dispersion relations. Transverse modes are further divided into type I and type II corresponding to TE and TM modes in the massless case. For general magnetodielectric media, we argue that the correct boundary conditions are the continuities of H{sub ||}, {phi}, A, and {partial_derivative}{sub x}A{sub x}, where x is the direction normal to the plates. Although there are type I transverse modes that satisfy all the boundary conditions, it is impossible to find type II transverse modes or longitudinal modes that satisfy all the boundary conditions. To circumvent this problem, type II transverse modes and longitudinal modes have to be considered together. We call the contribution to the Casimir energy from type I transverse modes TE contribution, and the contribution from the superposition of type II transverse modes and longitudinal modes TM contribution. Their massless limits give, respectively, the TE and TM contributions to the Casimir energy of a massless vector field. The limit wheremore » the plates become perfectly conducting is discussed in detail. For the special case where the background has a unity refractive index, it is shown that the TM contribution to the Casimir energy can be written as a sum of contributions from two different types of modes, corresponding to type II discrete modes and type III continuum modes discussed by Barton and Dombey [G. Barton and N. Dombey, Ann. Phys. (N.Y.) 162, 231 (1985).]. For general background, this splitting does not work. The limit where both plates become infinitely permeable and the limit where one plate becomes perfectly conducting and one plate becomes infinitely permeable are also investigated.« less

Geodesic acoustic modes and zonal flows in toroidally rotating tokamak plasmas

The effect of equilibrium toroidal rotation on the rotational eigen-modes in large aspect ratio tokamak is studied. The case of equilibrium with uniform plasma density on magnetic surfaces is considered. It is shown that the toroidal rotation results in a frequency up-shift of ordinary Geodesic Acoustic Modes. A new unstable low frequency branch of the continuum modes is found. This mode appears as a consequence of the non-uniform plasma pressure created by the centrifugal force on the magnetic surfaces. This mode represents a linear eigen-mode counterpart of Zonal Flow modes. It is shown that the growth rate of such a mode increases with the increase of the angular velocity of toroidal rotation.

Casimir effect of electromagnetic field in Randall-Sundrum spacetime

We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using the scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under the 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.

Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbor interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain system for a wide range of spectral functions and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short-range interactions of the effective chain system permit these open-quantum systems to be efficiently simulated by the density matrix renormalization group methods.

Fano resonances in nanoscale structures

Modern nanotechnology allows one to scale down various important devices (sensors, chips, fibers, etc.) and thus opens up new horizons for their applications. The efficiency of most of them is based on fundamental physical phenomena, such as transport of wave excitations and resonances. Short propagation distances make phase-coherent processes of waves important. Often the scattering of waves involves propagation along different paths and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different physical settings. The purpose of this review is to relate resonant scattering to Fano resonances, known from atomic physics. One of the main features of the Fano resonance is its asymmetric line profile. The asymmetry originates from a close coexistence of resonant transmission and resonant reflection and can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes. The basic concepts of Fano resonances are introduced, their geometrical and/or dynamical origin are explained, and theoretical and experimental studies of light propagation in photonic devices, charge transport through quantum dots, plasmon scattering in Josephson-junction networks, and matter-wave scattering in ultracold atom systems, among others are reviewed.

Wave-action conservation law for eigenmodes and continuum modes

Invariance of wave-action for eigenmodes and continuum modes around quasistationary equilibrium state is investigated in a general framework that allows for the ideal magnetohydrodynamic system and the Vlasov–Maxwell system. By utilizing the averaging method for the variational principle, the wave-action of each mode is shown to be conserved if its frequency (spectrum) is sufficiently separated from other ones, whereas some conservative exchange of the wave-action may occur among the modes with close frequencies. This general conservation law is, as an example, demonstrated for a situation where the Landau damping (or growth) occurs due to a resonance between an eigenmode and a continuum mode. The damping (or growth) rate is closely related to the spectral linewidth (equal to phase mixing rate) of the continuum mode, which can be estimated by the invariance of wave-action without invoking the conventional analytic continuation of the dispersion relation.

Fishbone modes in compressible plasmas

It is shown that there exist two types of m = n = 1 fishbone modes with frequencies significantly exceeding the frequency of the conventional fishbone instability. One of them is the resonance continuum mode (RCM), and the other is the non-resonance gap mode (NGM). They are associated with the trapped energetic ions and arise due to plasma compressibility. The spatial structure of the RCM may differ considerably from the rigid kink displacement inherent in the conventional fishbone mode.

On the theory of Brownian coagulation

The traditional diffusion approach for calculation of the collision frequency function for coagulation of Brownian particles is critically analyzed and shown to be valid only in the particular case of coalescence of small particles with large ones and inapplicable to calculation of the coalescence rate for particles of comparable sizes. It is shown that coalescence of Brownian particles generally occurs in the kinetic regime (realized under condition of homogeneous spatial distribution of particles), however, the expression for the collision frequency function in the continuum mode of the kinetic regime formally coincides with the standard expression derived in the diffusion regime for the particular case of large and small particles. This explains the validity of the traditional form of the coagulation rate equation in a wide range of parameters, corresponding to the continuum mode. Transition from the continuum to the free molecular mode can be described by the interpolation expression derived within the new analytical approach with fitting parameters that can be specified numerically, avoiding semi-empirical approach of existing models.

Connection between the two branches of the quantum two-stream instability across the k space

The stability of two quantum counterstreaming electron beams is investigated within the quantum plasma fluid equations for arbitrarily oriented wave vectors k. The analysis reveals that the two quantum two-stream unstable branches are indeed connected by a continuum of unstable modes with oblique wave vectors. Using the longitudinal approximation, the stability domain for any k is analytically explained, together with the growth rate.

Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics

Using Fourier optics, we retrieve the wavevector dependence of the third-harmonic (green) light generated in a slow light silicon photonic crystal waveguide. We show that quasi-phase matching between the third-harmonic signal and the fundamental mode is provided in this geometry by coupling to the continuum of radiation modes above the light line. This process sustains third-harmonic generation with a relatively high efficiency and a substantial bandwidth limited only by the slow light window of the fundamental mode. The results give us insights into the physics of this nonlinear process in the presence of strong absorption and dispersion at visible wavelengths where bandstructure calculations are problematic. Since the characteristics (e.g. angular pattern) of the third-harmonic light primarily depend on the fundamental mode dispersion, they could be readily engineered.

Quantum field theory, gravity and cosmology in a fractal universe

We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet regime where spacetime has Hausdorff dimension 2 to an infrared limit coinciding with a standard $D$-dimensional field theory. We discuss the properties of a scalar field model at classical and quantum level. Classically, the field lives on a fractal which exchanges energy-momentum with the bulk of integer topological dimension D. Although an observer experiences dissipation, the total energy-momentum is conserved. The field spectrum is a continuum of massive modes. The gravitational sector and Einstein equations are discussed in detail, also on cosmological backgrounds. We find ultraviolet cosmological solutions and comment on their implications for the early universe.