Critical Coupling Constant Research Articles

Synchronization of two indirectly coupled singly resonant optical parametric oscillators

We analyse a system of a singly resonant optical parametric oscillator for a second order nonlinear material. First, we show that the dynamics of the resonating cavity signal mode can be expressed by a Stuart–Landau oscillator, for a certain pumping powers close to the threshold. Second, we couple two optical parametric oscillators indirectly via a cold resonator. When the condition of a weak coupling is satisfied, the limit-cycle of each oscillator is unaltered, and the system is described by a coupled phase oscillator model (Kuramoto model), where a frequency synchronization of the two oscillators occurs at a critical coupling constant.

Reduced QED with Few Planes and Fermion Gap Generation.

The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of a few atomically thick layers, and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced theory describes charged fermions confined to N planes and contains N vector fields with Maxwell's action modified by non-local form factors whose explicit form is determined. Taking into account the polarization function, the explicit formulae for the screened electromagnetic interaction are presented in the case of two and three layers. For a heterostructure with two atomically thick layers and charged fermions described by the massless Dirac equation, the dynamical gap generation of the excitonic type is studied. It is found that additional screening due to the second layer increases the value of the critical coupling constant for the gap generation compared to that in graphene.

Color superconductivity on the lattice — analytic predictions from QCD in a small box

We investigate color superconductivity on the lattice using the gap equation for the Cooper pair condensate. The weak coupling analysis is justified by choosing the physical size of the lattice to be smaller than the QCD scale, while keeping the aspect ratio of the lattice small enough to suppress thermal excitations. In the vicinity of the critical coupling constant that separates the superconducting phase and the normal phase, the gap equation can be linearized, and by solving the corresponding eigenvalue problem, we obtain the critical point and the Cooper pair condensate without assuming its explicit form. The momentum components of the condensate suggest spatially isotropic s-wave superconductivity with Cooper pairs formed by quarks near the Fermi surface. The chiral symmetry in the massless limit is spontaneously broken by the Cooper pair condensate, which turns out to be dominated by the scalar and the pseudo-scalar components. Our results provide useful predictions, in particular, for future lattice simulations based on methods to overcome the sign problem such as the complex Langevin method.

Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation

We consider reduced quantum electrodynamics ( {mathrm{RQED}}_{d_{gamma },{d}_e} ) a model describing fermions in a de-dimensional space-time and interacting via the exchange of massless bosons in dγ-dimensions (de ≤ dγ). We compute the two-loop mass anomalous dimension, γm, in general {mathrm{RQED}}_{4,{d}_e} with applications to RQED4,3 and QED4. We then proceed on studying dynamical (parity-even) fermion mass generation in {mathrm{RQED}}_{4,{d}_e} by constructing a fully gauge-invariant gap equation for {mathrm{RQED}}_{4,{d}_e} with γm as the only input. This equation allows for a straightforward analytic computation of the gauge-invariant critical coupling constant, αc, which is such that a dynamical mass is generated for αr> αc, where αr is the renormalized coupling constant, as well as the gauge-invariant critical number of fermion flavours, Nc, which is such that αc → ∞ and a dynamical mass is generated for N < Nc. For RQED4,3, our results are in perfect agreement with the more elaborate analysis based on the resolution of truncated Schwinger-Dyson equations at two-loop order. In the case of QED4, our analytical results (that use state of the art five-loop expression for γm) are in good quantitative agreement with those obtained from numerical approaches.

Polaronic signatures in pristine phosphorene

We investigate polaronic effects in a monolayer black phosphorus (or phosphorene) due to the charge carrier--intrinsic phonons interaction. We employ a microscopic model to describe vibrational spectra and electron-phonon interactions within the tight-binding approach. Our adiabatic solution for polarons suggests the critical coupling constant of ${\ensuremath{\lambda}}_{c}=3.0$ for polaron self-trapping in this anisotropic material. We report nonadiabatic calculations for the band-gap renormalization and the effective mass enhancement as a function of temperature and a range of electron-phonon coupling strengths. Our results demonstrate a surprising large band-gap renormalization, even for the lower bound of the electron-phonon coupling strength reported in the literature. We find that optical phonons give the dominant contributions to the polaronic effect.

Pattern in nonlinearly coupled network of identical Thomas oscillators

We have investigated synchronized patterns in a network of Thomas oscillators coupled with sinusoidal nonlinear and linear couplings. Patterns like chimera and cluster states are not only observed for many nonlocally coupled oscillators, it is also observed for nearly local coupled network topology in the case of nonlinear coupling. As coupling radius increases, the critical coupling constant for complete synchronization decreases. Crater-like structure is also observed in the snapshot in the case of nonlinear coupling only which agrees with similar observation found in the study of active Brownian particles using the stochastic method. The critical number of oscillators for the onset of chimera is forty and the infinite limit is found to be hundred. No chimera is observed in the zero friction limit due to hyperchaotic motion with large amplitude oscillations, but there is a sharp transition from disorder to order distribution.

Solitary waves dynamic for Davydov α-helical protein model: Effects of localized and periodic inhomogeneities.

We describe the dynamic of excitons through single inhomogeneous α-helical proteins with off-diagonal and diagonal couplings. Inhomogeneities considered are either localized or periodic. Intensive numerical simulations carried show stable structures and allow us to single out important features of excitons dynamic. In the absence of inhomogeneities, the interplay between off-diagonal and diagonal couplings leads to two distinct types of solitary waves. Bright solitary waves correspond to an off-diagonal coupling constant lower than a critical diagonal coupling constant, while dark solitary waves are obtained in the opposite case. Inclusion of inhomogeneities profoundly affects the profiles, amplitudes, and energies transported by the waves. For relatively small strength of inhomogeneities, only the profiles of the waves significantly change, the other properties remaining almost unchanged. Large strength inhomogeneities sensitively twist the profiles and increase amplitudes and energies of the waves. Our study suggests that small strength inhomogeneities allow a coherent transport of energy and the biological functions remain unchanged, but large strengths of inhomogeneities affect the biological functioning of the α-helical protein chains. Hence, large strengths of inhomogeneities may amplify the energy of the molecule and could be used to treat some diseases.

Atomic collapse in disordered graphene quantum dots

In this paper, we numerically study a Coulomb impurity problem for interacting Dirac fermions restricted in disordered graphene quantum dots. In the presence of randomly distributed lattice defects and spatial potential fluctuations, the response of the critical coupling constant for atomic collapse is mainly investigated by local density of states calculations within the extended mean-field Hubbard model. We find that both types of disorder cause an amplification of the critical threshold. As a result, up to thirty-four percent increase in the critical coupling constant is reported. This numerical result may explain why the Coulomb impurities remain subcritical in experiments, even if they are supercritical in theory. Our results also point to the possibility that atomic collapse can be observed in defect-rich samples such as Ar$^{+}$ ion bombarded, He$^{+}$ ion irradiated, and hydrogenated graphene.

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions in largeNexpansion

Recently the renormalization of the band gap $m$, in both WSe$_2$ and MoS$_2$, has been experimentally measured as a function of the carrier concentration $n$. The main result establishes a decreasing of hundreds of meV, in comparison with the bare band gap, as the carrier concentration increases. These materials are known as transition metal dichalcogenides and their low-energy excitations are, approximately, described by the massive Dirac equation. Using Pseudo Quantum Electrodynamics (PQED) to describe the electromagnetic interaction between these quasiparticles and from renormalization group analysis, we obtain that the renormalized mass describes the band gap renormalization with a function given by $m(n)/m_0=(n/n_0)^{C_\lambda/2}$, where $m_0=m(n_0)$ and $C_\lambda$ is a function of the coupling constant $\lambda$. We compare our theoretical results with the experimental findings for WSe$_2$ and MoS$_2$, and we conclude that our approach is in agreement with these experimental results for reasonable values of $\lambda$. In addition we introduced a Gross-Neveu (GN) interaction which could simulate an disorder/impurity-like microscopic interaction. In this case, we show that there exists a critical coupling constant, namely, $\lambda_c \approx 0,66$ in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For $\lambda>\lambda_c$, the renormalized mass decreases while for $\lambda<\lambda_c$ it increases with the carrier concentration.

Effective-Field Approach to Magnetic Properties of Spin-1 System in XXZ Model with Single-Ion Uniaxial Anisotropy

In the XXZ Heisenberg model with the positive single-ion uniaxial anisotropy D, magnetic properties of the spin-1 system are studied by the one-site effective-field theory, which takes account of the effect of on-site spin fluctuations in the direction of the magnetization, neglected in the mean-field approximation. At temperatures above the transition point, a spin susceptibility is generally derived, and in the temperature range much above the exchange coupling constants and D, the susceptibility is shown to agree with that given by the mean-field approximation, leading to the correct Curie–Weiss law in accordance with the result in the high-temperature expansion. In the present case where the easy-plane of magnetization is xy-plane, the critical exchange coupling constant for the ferromagnetic order is Jxc/D = 0.182, which is larger than the value by the mean-field approximation 0.125 due to the effect of quantum-spin fluctuations. Characteristic behaviors of the susceptibility in the absence of the ferromagnetic order are explored in detail. The results are applied to an analysis for spin–lattice relaxation rate \(T_{1}^{ - 1}\) in Li9V3(P2O7)3(PO4)2, which is shown to be definitely linear in the square root of the susceptibility in the x-direction, \(T_{1}^{ - 1} \propto \chi _{\text{s}}^{x}{}^{1/2}\), consistent with the theory by Moriya.

Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions

We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the Pseudo Quantum Electrodynamics (PQED) and the latter is given by the so-called Gross-Neveu action. We apply the Hubbard-Stratonovich transformation and the large$-N_f$ expansion in our model to obtain a Yukawa action. Thereafter, the presence of a symmetry broken phase is inferred from the non-perturbative Schwinger-Dyson equation for the electron propagator. This is the physical solution whenever the fine-structure constant is larger than a critical value $\alpha_c(D N_f)$. In particular, we obtain the critical coupling constant $\alpha_c\approx 0.36$ for $D N_f=8$., where $D=2,4$ corresponds to the SU(2) and SU(4) cases, respectively, and $N_f$ is the flavor number. Our results show a decreasing of the critical coupling constant in comparison with the case of pure electromagnetic interaction, thus yielding a more favorable scenario for the occurrence of dynamical symmetry breaking. For two-dimensional materials,in application in condensed matter systems, it implies an energy gap at the Dirac points or valleys of the honeycomb lattice.

Monte Carlo study of Dirac semimetals phase diagram

In this paper the phase diagram of Dirac semimetals is studied within lattice Monte-Carlo simulation. In particular, we concentrate on the dynamical chiral symmetry breaking which results in semimetal/insulator transition. Using numerical simulation we determined the values of the critical coupling constant of the semimetal/insulator transition for different values of the anisotropy of the Fermi velocity. This measurement allowed us to draw tentative phase diagram for Dirac semimetals. It turns out that within the Dirac model with Coulomb interaction both Na$_3$Bi and Cd$_3$As$_2$ known experimentally to be Dirac semimetals would lie deeply in the insulating region of the phase diagram. It probably shows a decisive role of screening of the interelectron interaction in real materials, similar to the situation in graphene.

Magnetic properties of spin-1/2 Fermi gases with ferromagnetic interaction

We investigate the magnetic properties of spin-$1/2$ charged Fermi gases with ferromagnetic coupling via mean-field theory, and find the interplay among the paramagnetism, diamagnetism and ferromagnetism. Paramagnetism and diamagnetism compete with each other. When increasing the ferromagnetic coupling the spontaneous magnetization occurs in a weak magnetic field. The critical ferromagnetic coupling constant of the paramagnetic phase to ferromagnetic phase transition increases linearly with the temperature. Both the paramagnetism and diamagnetism increase when the magnetic field increases. It reveals the magnetization density $\bar M$ increases firstly as the temperature increases, and then reaches a maximum. Finally the magnetization density $\bar M$ decreases smoothly in the high temperature region. The domed shape of the magnetization density $\bar M$ variation is different from the behavior of Bose gas with ferromagnetic coupling. We also find the curve of susceptibility follows the Curie-Weiss law, and for a given temperature the susceptibility is directly proportional to the Land\'{e} factor.

System of Schwinger-Dyson equations and asymptotic behavior in the Euclidean region

A system of Schwinger-Dyson equations for the model of scalar-field interaction is studied in a deep Euclidean region. It is shown that there exists a critical coupling constant that separates the weak-coupling region characterized by the asymptotically free behavior and the strong-coupling region, where the asymptotic behavior of field propagators becomes ultralocal.

Critical temperature of the Ising ferromagnet on the fcc, hcp, and dhcp lattices

By an extensive Monte-Carlo calculation together with the finite-size-scaling and the multiple histogram method, the critical coupling constant (Kc=J/kBTc) of the Ising ferromagnet on the fcc, hcp, and double hcp (dhcp) lattices were obtained with unprecedented precision: Kcfcc=0.1020707(2), Kchcp=0.1020702(1), and Kcdhcp=0.1020706(2). The critical temperature Tc of the hcp lattice is found to be higher than those of the fcc and the dhcp lattice. The dhcp lattice seems to have higher Tc than the fcc lattice, but the difference is within error bars.

Acoustic Polaron in Free-Standing Slabs

The ground-state energy and its derivate of the acoustic polaron in free-standing slab are calculated by using the Huybrechts-like variational approach. The criteria for presence of the selftrapping transition of the acoustic polaron in free-standing slabs are determined qualitatively. The critical coupling constant for the discontinuous transition from a quasi-free state to a trapped state of the acoustic polaron in free-standing slabs tends to shift toward the weaker electronphonon coupling with the increasing cutoff wave-vector. Detailed numerical results confirm that the self-trapping transition of holes is expected to occur in the free-standing slabs of wide-bandgap semi-conductors.

Double-scaling limit of the O(N)-symmetric anharmonic oscillator

In an earlier paper it was argued that the conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative and thus the integral representing the partition function of the critical theory does not exist. In this earlier paper it was shown that for a zero-dimensional O(N)-symmetric quantum field theory one can avoid this difficulty if one replaces the original quartic theory by its -symmetric analog. In the current paper an O(N)-symmetric quartic quantum field theory in one time dimension and zero space dimensions (that is, O(N)-symmetric quantum mechanics) is studied using the Schrödinger equation. It is shown that the global -symmetric formulation of this differential equation provides a consistent way to perform the double-scaling limit of the O(N)-symmetric anharmonic oscillator. The physical nature of the critical behavior is explained by studying the -symmetric quantum theory and the corresponding and equivalent Hermitian quantum theory.

Asymptotic behavior and critical coupling in the scalar Yukawa model from Schwinger–Dyson equations

A sequence of n-particle approximations for the system of Schwinger–Dyson equations is investigated in the model of a complex scalar field ϕ and a real scalar field χ with the interaction gϕ*ϕχ. In the first non-trivial two-particle approximation, the system is reduced to a system of two nonlinear integral equations for propagators. The study of this system shows that for equal masses a critical coupling constant exists, which separates the weak- and strong-coupling regions with the different asymptotic behavior for deep Euclidean momenta. In the weak-coupling region (), the propagators are asymptotically free, which corresponds to the wide-spread opinion about the dominance of perturbation theory for this model. At the critical point, the asymptotics of propagators are ∼1/p. In the strong-coupling region (), the propagators are asymptotically constant, which corresponds to the ultra-local limit. For unequal masses, the critical point transforms into a segment of values, in which there are no solutions with a self-consistent ultraviolet behavior without Landau singularities.

-symmetric interpretation of double-scaling

The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian defines a quantum theory with an upside-down potential whose energy appears to be unbounded below. Worse yet, the integral representation of the partition function of the theory does not exist. It is shown that one can avoid these difficulties if one replaces the original theory by its -symmetric analog. For a zero-dimensional O(N)-symmetric quartic vector model the partition function of the -symmetric analog is calculated explicitly in the double-scaling limit.

The fate of the Wilson-Fisher fixed point in non-commutative ϕ4

In this article we study non-commutative vector sigma model with the most general ϕ4 interaction on Moyal-Weyl spaces. We compute the 2- and 4-point functions to all orders in the large N limit and then apply the approximate Wilson renormalization group recursion formula to study the renormalized coupling constants of the theory. The non-commutative Wilson-Fisher fixed point interpolates between the commutative Wilson-Fisher fixed point of the Ising universality class which is found to lie at zero value of the critical coupling constant a* of the zero dimensional reduction of the theory, and a novel strongly interacting fixed point which lies at infinite value of a* corresponding to maximal non-commutativity beyond which the two-sheeted structure of a* as a function of the dilation parameter disappears.