Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur

Spin Current and Current-Induced Spin Transfer Torque in Ferromagnet-Quantum Dot-Ferromagnet Coupled Systems

Based on Keldysh's nonequilibrium Green function method, the spin-dependent transport properties in a ferromagnet-quantum dot (QD)-ferromagnet coupled system are investigated. It is shown the spin current shows quite different characteristics from its electrical counterpart, and by changing the relative orientation of both magnetizations, it can change its magnitude even sign. The current-induced spin transfer torque (CISTT) is uncovered to be greatly enhanced when the bias voltage meets with the discrete levels of the QD at resonant positions. The relationship between the CISTT, the electrical current and the spin current is also addressed.Comment: 21 pages, 8 figure

Eliashberg theory of excitonic insulating transition in graphene

A sufficiently strong Coulomb interaction may open an excitonic fermion gap and thus drive a semimetal-insulator transition in graphene. In this paper, we study the Eliashberg theory of excitonic transition by coupling the fermion gap equation self-consistently to the equation of vacuum polarization function. Including the fermion gap into polarization function increases the effective strength of Coulomb interaction because it reduces the screening effects due to the collective particle-hole excitations. Although this procedure does not change the critical point, it leads to a significant enhancement of the dynamical fermion gap in the excitonic insulating phase. The validity of the Eliashberg theory is justified by showing that the vertex corrections are suppressed at large $N$ limit.Comment: 8 pages, 6 figure

Fate of non-Fermi liquid behavior in QED3_{3} at finite chemical potential

The damping rate of two-dimensional massless Dirac fermions exhibit non-Fermi liquid behavior, $\propto \epsilon^{1/2}$, due to gauge field at zero temperature and zero chemical potential. We study the fate of this behavior at finite chemical potential. We fist calculate explicitly the temporal and spatial components of vacuum polarization functions. The analytical expressions imply that the temporal component of gauge field develops a static screening length at finite chemical potential while the transverse component remains long-ranged owing to gauge invariance. We then calculate the fermion damping rate and show that the temporal gauge field leads to normal Fermi liquid behavior but the transverse gauge field leads to non-Fermi liquid behavior $\propto \epsilon^{2/3}$ at zero temperature. This energy-dependence is more regular than $\propto \epsilon^{1/2}$ and does not change as chemical potential varies.Comment: 12 pages, 1 figur

Dark-bright gap solitons in coupled-mode one-dimensional saturable waveguide arrays

In the present work, we consider the dynamics of dark solitons as one mode of a defocusing photorefractive lattice coupled with bright solitons as a second mode of the lattice. Our investigation is motivated by an experiment which illustrates that such coupled states can exist with both components in the first gap of the linear band spectrum. This finding is further extended by the examination of different possibilities from a theoretical perspective, such as symbiotic ones where the bright component is supported by states of the dark component in the first or second gap, or non-symbiotic ones where the bright soliton is also a first-gap state coupled to a first or second gap state of the dark component. While the obtained states are generally unstable, these instabilities typically bear fairly small growth rates which enable their observation for experimentally relevant propagation distances

Thermodynamic Curvature of the BTZ Black Hole

Some thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole are studied to get the effective dimension of its corresponding statistical model. For this purpose, we make use of the geometrical approach to the thermodynamics: Considering the black hole as a thermodynamic system with two thermodynamic variables (the mass $M$ and the angular momemtum $J$), we obtain two-dimensional Riemannian thermodynamic geometry described by positive definite Ruppeiner metric. From the thermodynamic curvature we find that the extremal limit is the critical point. The effective spatial dimension of the statistical system corresponding to the near-extremal BTZ black holes is one. Far from the extremal point, the effective dimension becomes less than one, which leads to one possible speculation on the underlying structure for the corresponding statistical model.Comment: 19 pages, LaTeX with revtex macro, 4 figures in eps file

Spin-Polarized Transport in Ferromagnet-Marginal Fermi Liquid Systems

Spin-polarized transport through a marginal Fermi liquid (MFL) which is connected to two noncollinear ferromagnets via tunnel junctions is discussed in terms of the nonequilibrium Green function approach. It is found that the current-voltage characteristics deviate obviously from the ohmic behavior, and the tunnel current increases slightly with temperature, in contrast to those of the system with a Fermi liquid. The tunnel magnetoresistance (TMR) is observed to decay exponentially with increasing the bias voltage, and to decrease slowly with increasing temperature. With increasing the coupling constant of the MFL, the current is shown to increase linearly, while the TMR is found to decay slowly. The spin-valve effect is observed.Comment: 5 pages, 6 figures, Phys. Rev. B 71, 064412 (2005

Tunable Fano effect in parallel-coupled double quantum dot system

With the help of the Green function technique and the equation of motion approach, the electronic transport through a parallel-coupled double quantum dot(DQD) is theoretically studied. Owing to the inter-dot coupling, the bonding and antibonding states of the artificial quantum-dot-molecule may constitute an appropriate basis set. Based on this picture, the Fano interference in the conductance spectra of the DQD system is readily explained. The possibility of manipulating the Fano lineshape in the tunnelling spectra of the DQD system is explored by tuning the dot-lead coupling, the inter-dot coupling, the magnetic flux threading the ring connecting dots and leads, and the flux difference between two sub-rings. It has been found that by making use of various tuning, the direction of the asymmetric tail of Fano lineshape may be flipped by external fields, and the continuous conductance spectra may be magnetically manipulated with lineshape retained. More importantly, by adjusting the magnetic flux, the function of two molecular states can be exchanged, giving rise to a swap effect, which might play a role as a qubit in the quantum computation.Comment: 9 pages, 10 figure

First- and Second-Order Phase Transitions, Fulde-Ferrel Inhomogeneous State and Quantum Criticality in Ferromagnet/Superconductor Double Tunnel Junctions

First- and second-order phase transitions, Fulde-Ferrel (FF) inhomogeneous superconducting (SC) state and quantum criticality in ferromagnet/superconductor/ferromagnet double tunnel junctions are investigated. For the antiparallel alignment of magnetizations, it is shown that a first-order phase transition from the homogeneous BCS state to the inhomogeneous FF state occurs at a certain bias voltage $V^{\ast}$; while the transitions from the BCS state and the FF state to the normal state at $V_{c}$ are of the second-order. A phase diagram for the central superconductor is presented. In addition, a quantum critical point (QCP), $$, is identified. It is uncovered that near the QCP, the SC gap, the chemical potential shift induced by the spin accumulation, and the difference of free energies between the SC and normal states vanish as $$ with the quantum critical exponents $z\nu =1/2$, 1 and 2, respectively. The tunnel conductance and magnetoresistance are also discussed.Comment: 5 pages, 4 figures, Phys. Rev. B 71, 144514 (2005

Dual Actions for Born-Infeld and Dp-Brane Theories

Dual actions with respect to U(1) gauge fields for Born-Infeld and $Dp$-brane theories are reexamined. Taking into account an additional condition, i.e. a corollary to the field equation of the auxiliary metric, one obtains an alternative dual action that does not involve the infinite power series in the auxiliary metric given by ref. \cite{s14}, but just picks out the first term from the series formally. New effective interactions of the theories are revealed. That is, the new dual action gives rise to an effective interaction in terms of one interaction term rather than infinite terms of different (higher) orders of interactions physically. However, the price paid for eliminating the infinite power series is that the new action is not quadratic but highly nonlinear in the Hodge dual of a $(p-1)$-form field strength. This non-linearity is inevitable to the requirement the two dual actions are equivalent.Comment: v1: 11 pages, no figures; v2: explanation of effective interactions added; v3: concision made; v4: minor modification mad