Weak Coupling Case Research Articles

Effect of interactions on Dirac points in organic solids

We examine the effect of inter-site interactions in the anisotropic triangular lattice with α - type symmetry, which has a linear energy dispersion called Dirac point. Charge disproportionation without inversion symmetry breaking is made a sharp distinction from charge order which is accompanied by the symmetry breaking, and only the latter is found to be responsible for the destruction of Dirac points. We also show that in the weak coupling case, the small density of states near the Fermi level protects the Dirac points from the instability towards charge order.

ENTROPY IN SCALAR O(N) MODEL WITH A SPONTANEOUSLY BROKEN SYMMETRY

We investigate the entropy in a scalar O(N) model with a spontaneously broken symmetry. The Cornwall–Jackiw–Tomboulis formalism is applied to derive the entropy in the Hartree and Hartree–Fock approximations. In contrast to the Hartree approximation where the particles are quasiparticles with vanishing decay width, the Hartree–Fock approximation contains exchange contributions, which lead to nonzero decay width. We find that the sunset diagrams contribution is very small. Furthermore, the decay widths from these diagrams are discussed in the weak and strong coupling cases.

Weak coupling regime of the Landau-Zener transition for association of an atomic Bose-Einstein condensate

In the framework of a basic semiclassical time-dependent nonlinear two-state problem, we study the weak coupling limit of the nonlinear Landau-Zener transition at coherent photo- and magneto-association of an atomic Bose-Einstein condensate. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct an accurate analytic approximation describing time dynamics of the coupled atom-molecular system for the case of weak coupling. The approximation is written in terms of the solution to an auxiliary linear Landau-Zener problem with some effective Landau-Zener parameter. The dependence of this effective parameter on the input Landau-Zener parameter is found to be unexpected: as the generic Landau-Zener parameter increases, the effective Landau-Zener parameter first monotonically increases (starting from zero), reaches its maximal value and then monotonically decreases again reaching zero at some point. The constructed approximation quantitatively well describes many characteristics of the time dynamics of the system, in particular, it provides a highly accurate formula for the final transition probability to the molecular state. The present result for the final transition probability improves the accuracy of the previous approximation by Ishkhanyan et al. [Phys. Rev. A 69, 043612 (2004); J. Phys. A 38, 3505 (2005)] by order of magnitude.

Zero and First Sound in Normal Fermi Systems

On the basis of a moment method, general solutions of a linearized Boltzmann equation for a normal Fermi system are investigated. In particular, we study the sound velocities and damping rates as functions of the temperature and the coupling constant. In the extreme limits of collisionless and hydrodynamic regimes, eigenfrequency of sound mode obtained from the moment equations reproduces the well-known results of zero sound and first sound. In addition, the moment method can describe crossover between those extreme limits at finite temperatures. Solutions of the moment equations also involve a thermal diffusion mode. From solutions of these equations, we discuss excitation spectra corresponding to the particle-hole continuum as well as collective excitations. We also discuss a collective mode in a weak coupling case.

Correlations in the ground state of the one-dimensional Hubbard model

With eigenfunctional theory and a rigorous expression of exchange-correlation energy of a general interacting electron system, we study the ground state properties of the one-dimensional Hubbard model, and calculate the ground-state energy as well as the charge gap at half-filling for arbitrary coupling strength u = U / ( 4 t ) and electron density n c . We find that the simple linear approximation of the phase field works well in weak coupling case, but it becomes inappropriate as the on-site Coulomb interaction becomes strong where the fluctuations of the bosonic auxiliary field are strong. Then we propose a new scheme by adding Gutzwiller projection which suppresses the density fluctuations and the new results are quite close to the exact ones up to considerably strong coupling strength u = 3.0 and for arbitrary electron density n c . Our calculation scheme is proved to be effective for strongly correlated electron systems in one dimension, and its extension to higher dimensions is straightforward.

Emergence of quantum hydrodynamic sound mode of a quantum Brownian particle in a one-dimensional molecular chain

We have theoretically investigated a long-time transport process of a quantum Brownian particle interacting with a thermal phonon field in a one-dimensional molecular chain. A kinetic equation is derived from a quantum Liouville equation in a weak-coupling case by applying a complex spectral representation of Liouvillean. Due to a characteristic Poincar\'e resonance for a quantum one-dimensional system, there are an infinite number of degeneracy for collision invariants. In the hydrodynamic situation, the degeneracy is lifted by the first order of perturbation of the flow term, resulting in a new hydrodynamic mode, i.e., quantum hydrodynamic sound mode. It is found that the time evolution of the quantum hydrodynamic sound mode obeys a macroscopic linear wave equation for the probability distribution of the quantum particle. It is remarkable that the stability of the wave packet of the sound wave increases as temperature increases. As a demonstration, the sound wave of the minimum uncertainty wave packet is theoretically analyzed.

Effects of periodic modulation on the nonlinear Landau–Zener tunneling

We study the Landau–Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.

Configurations of Equivalent Electrons

We derive here a comprehensive set of formulas for determining the overall spin and spatial symmetry of wave functions arising from a partially filled degenerate orbital. We extend the usual arguments for the case of weak coupling between spin and spatial angular momenta to the jj-coupling case.

Negative refractive index response of weakly and strongly coupled optical metamaterials

We present a detailed study of the retrieved optical parameters, electrical permittivity $\ensuremath{\epsilon}$, magnetic permeability $\ensuremath{\mu}$, and refractive index $n$ of the coupled-fishnet metamaterial structures as a function of the separation between layers. For the weak-coupling case, the retrieved parameters are very close to the one-functional-layer results and converge relatively fast. For the strong-coupling case, the retrieved parameters are completely different from the one-unit fishnet results. We also demonstrate that the high value of the figure of merit $[\text{FOM}=|\text{Re}(n)/\text{Im}(n)|]$ for the strongly coupled structures is due to the fact that the real part of the negative $n$ moves away from the maximum of the imaginary part of $n$ (close to the resonance), where the losses are high.

One-dimensional δ-function attractive Fermi gas in an external magnetic field

We investigate the ground-state properties of a one-dimensional spin-1/2 fermionic atoms interacting through the attractive δ-function potential in an external magnetic field. By the thermal Bethe ansatz method, the integral equations for the dressed energies are formulated. Those integral equations at zero-temperature are solved in the power series forms of rapidity and momentum for both strong and weak coupling cases. The magnetization as a function of the coupling constant and the external field is also obtained explicitly. Based on the analytic results, quantum phase transitions are identified among three phases, an unpolarized fully paired state, a fully polarized normal ferromagnetic state and a mixed state of paired and unpaired atoms.

AC field-controlled Andreev tunneling through a serially-coupled double quantum dot system

AC field-controlled Andreev tunneling through two serially-coupled quantum dots are investigated theoretically by using the nonequilibrium Green's function method. The photon-assisted Andreev tunneling is studied in detail. It is found that the average current depends distinctly on the interdot coupling. In the weak interdot coupling case, the average current versus the gate voltage exhibit negative peaks on the left-hand side and positive peaks on the right-hand side of the Fermi level. However, in the strong interdot coupling case, the current exhibit both negative and positive peaks on each side of the Fermi level. Furthermore, the system can function as an electron pump capable of transporting electrons through the resonant photon-assisted Andreev tunneling.

Vacuum Rabi Oscillation of an Atom without Rotating-Wave Approximation

We have investigated vacuum Rabi oscillation of an atom coupled with single-mode cavity field exactly, and compared the results with that of the Jaynes–Cummings (J–C) model. The results show that for resonant case, there is no Rabi oscillation for an atom. For small detuning and weak coupling case, the probability for the atom in excited state oscillates against time with different frequencies and amplitudes from that of the J-C model. It exhibits that the counter-rotating wave interaction could significantly effect the dynamic behaviour of the atom, even under the condition in which the RWA is considered to be justified.

Pulse Wave Propagation in a Large Number of Coupled Bistable Oscillators

A simple model of inductor-coupled bistable oscillators is shown to exhibit pulse wave propagation. We demonstrate numerically that there exists a pulse wave which propagates with a constant speed in comparatively wide parameter region. In particular, the propagating pulse wave can be observed in non-uniform lattice with noise. The propagating pulse wave can be observed for comparatively strong coupling case, and for weak coupling case no propagating pulse wave can be observed (propagation failure). We also demonstrate various interaction phenomena between two pulses.

Photophysics of Soret-Excited Tetrapyrroles in Solution. I. Metalloporphyrins: MgTPP, ZnTPP, and CdTPP

The photophysical behavior of three Soret-excited diamagnetic meso-substituted tetraphenylmetalloporphyrins, MgTPP, ZnTPP, and CdTPP, have been examined in a wide variety of solvents using both steady-state and femtosecond fluorescence upconversion methods. The S 2 population of MgTPP decays to S 1 on the time scale of a few picoseconds with unit S 2-S 1 internal conversion efficiency, and the decay rates conform to the weak coupling case of radiationless transition theory. The energy gap law parameters characterizing the coupling of the S 2 and S 1 states of MgTPP have been obtained. The most important accepting vibrational modes in the S 1 state are multiple in-plane C-C and C-N stretches in the 1200-1500 cm (-1) range. Net S 2-S 1 decay is the dominant decay path for ZnTPP and CdTPP as well, but the process occurs at rates that exceed (in the case of CdTPP, they vastly exceed) those predicted by weak interstate coupling. Alternate mechanisms for the radiationless decay of the S 2 states of ZnTPP and CdTPP have been explored. Large spin-orbit coupling constants and the presence of multiple, near-equiergic triplet states suggest that S 2-T n intersystem crossing might occur at rates competitive with internal conversion. However, the measured efficiencies of S 2-S 1 internal conversion show that, at most, only a few percent of the S 2 population of ZnTPP and no more than about 30% of the S 2 population of CdTPP can decay by a "dark" path such as intersystem crossing.

Statistics of resonances in a semi-infinite disordered chain

We study the average density of resonances (DOR) for a semi-infinite disordered chain, coupled to the outside world by a (semi-infinite) perfect lead. A set of equations is derived, which provides the general framework for calculating the average DOR, for an arbitrary disorder and coupling strength. These general equations are applied to the case of weak coupling and an asymptotically exact expression for the averaged DOR is derived, in the limit of small resonance width. This expression is universal, in the sense that it holds for any degree of disorder and everywhere in the (unperturbed) energy band.

Exact Analysis of a δ-Function Spin-1/2 Attractive Fermi Gas with an External Magnetic Field

We study the excitation spectrum of a one-dimensional δ-function attractive spin-1/2 fermions by the thermal Bethe ansatz method at zero temperature. The integral equation for the dressed energies of the system with an external magmatic field is solved in the form of power series. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. We also study the magnetization as a function of the coupling constant and the external field.

Weak-and strong-coupling limits of the two-dimensional Fröhlich polaron with spin-orbit Rashba interaction

The continuous progress in fabricating low-dimensional systems with large spin-orbit couplings has reached a point in which nowadays materials may display spin-orbit splitting energies ranging from a few to hundreds of meV. This situation calls for a better understanding of the interplay between the spin-orbit coupling and other interactions ubiquitously present in solids, in particular when the spin-orbit splitting is comparable in magnitude with characteristic energy scales such as the Fermi energy and the phonon frequency. In this article, the two-dimensional Fr\"ohlich electron-phonon problem is reformulated by introducing the coupling to a spin-orbit Rashba potential, allowing for a description of the spin-orbit effects on the electron-phonon interaction. The ground state of the resulting Fr\"ohlich-Rashba polaron is studied in the weak and strong coupling limits of the electron-phonon interaction for arbitrary values of the spin-orbit splitting. The weak coupling case is studied within the Rayleigh-Schr\"odinger perturbation theory, while the strong-coupling electron-phonon regime is investigated by means of variational polaron wave functions in the adiabatic limit. It is found that, for both weak and strong coupling polarons, the ground state energy is systematically lowered by the spin-orbit interaction, indicating that the polaronic character is strengthened by the Rashba coupling. It is also shown that, consistently with the lowering of the ground state, the polaron effective mass is enhanced compared to the zero spin-orbit limit. Finally, it is argued that the crossover between weakly and strongly coupled polarons can be shifted by the spin-orbit interaction.

Spontaneous emission properties of a quantum dot in an ultrahigh-Qcavity: Crossover from weak- to strong-coupling states and robust quantum interference

We theoretically discuss spontaneous emission properties of a quantum dot embedded in an ultrahigh-$Q$ microcavity, where a detuning between an excitation in the quantum dot and the cavity mode is taken into account. Both weak- and strong-coupling states are obtained under the ultrahigh-$Q$ condition. In the high-$Q$ weak-coupling case, the spontaneous emission spectrum shows a sharp dip, whose origin is a quantum interference. In the strong-coupling case, there is a region where both the Rabi splitting and the quantum interference contribute on an equal footing, referred to as a crossover region, where the spontaneous emission spectral shape is quite similar to that of the high-$Q$ weak-coupling state. The quantum interference is robust against the detuning.

Disentanglement of two qubits coupled to anXYspin chain: Role of quantum phase transition

We study the disentanglement evolution of two spin qubits which interact with a general $XY$ spin-chain environment. The dynamical process of the disentanglement is numerically and analytically investigated in the vicinity of a quantum phase transition (QPT) of the spin chain in both weak and strong coupling cases. We find that the disentanglement of the two spin qubits may be greatly enhanced by the quantum critical behavior of the environmental spin chain. We give a detailed analysis to facilitate the understanding of the QPT-enhanced decaying behavior of the coherence factor. Furthermore, the scaling behavior in the disentanglement dynamics is also revealed and analyzed.

Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping

This is the first one of a series of our papers theoretically studying the coherent control of photon transmission along the coupled resonator optical waveguide (CROW) by doping artificial atoms for various hybrid structures. We will provide the several approaches correspondingly based on Green function, the mean field method and spin wave theory et al. In the present paper we adopt the two-time Green function approach to study the coherent transmission photon in a CROW with homogeneous couplings, each cavity of which is doped by a two-level artificial atom. We calculate the two-time correlation function for photon in the weak-coupling case. Its poles predict the exact dispersion relation, which results in the group velocity coherently controlled by the collective excitation of the doping atoms. We emphasize the role of the population inversion of doping atoms induced by some polarization mechanism.