arXiv subjects

Shi-Dong Liang

Publications and source records attributed to Shi-Dong Liang.

At least 37 records · Page 2Linked to original sources

arXiv2021

Quantum Hall admittance in non-Hermitian systems

We propose a pair of the complex Berry curvatures associated with the non-Hermitian Hamiltonian and its Hermitian adjoint to reveal new physics in non-Hermitian systems. We give the complex Berry curvature and Berry phase for the two-dimensional non-Hermitian Dirac model. The imaginary part of the complex Berry phase induces the quantum Hall susceptance such that the quantum Hall conductance is generalized to quantum Hall admittance for non-Hermitian systems, which implies that the non-Hermiticity of systems could induce an intrinsic quantum capacitance or inductance of systems depending on the non-Hermitian parameters. We analyze the complex energy band structures of the two-dimensional non-Hermitian Dirac model and demonstrate the point and line gaps and their closings as the exceptional degeneracy of the energy bands in the parameter space, which are associated with topological phases. In the continuum limit, we obtain the complex Berry phase in the parameter space.

quant-ph↗

arXiv2020

Black hole solutions in modified gravity induced by quantum metric fluctuations

The inclusion of the quantum fluctuations of the metric in the geometric action is a promising avenue for the understanding of the quantum properties of gravity. In this approach the metric is decomposed in the sum of a classical and of a fluctuating part, of quantum origin, which can be generally expressed in terms of an arbitrary second order tensor, constructed from the metric, and from the thermodynamic quantities describing matter fields. In the present paper we investigate the effects of the quantum fluctuations on the spherically symmetric static black hole solutions of the modified field equations, obtained from a variational principle, by assuming that the quantum correction tensor is given by the coupling of a scalar field to the metric tensor. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, we obtain their solutions numerically. We detect the formation of a black hole from the presence of a singularity in the metric tensor components. Several models, corresponding to different functional forms of the scalar field potential, are considered. The thermodynamic properties of the black hole solutions (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also investigated.

gr-qc↗

arXiv2020

Phonon dispersions and electronic structures of two-dimensional IV-V compounds

One novel family of two-dimensional IV-V compounds have been proposed, whose dynamical stabilities and electronic properties have been systematically investigated using the density functional theory. Extending from our previous work, two phases of carbon phosphorus bilayers α- and β-C$_{2}$P$_{2}$ have been proposed. Both of them are dynamically stable and thermally stable at 300K. They possess intrinsic HSE gaps of 2.70 eV and 2.67 eV, respectively. Similar α- and β-C$_{2}$Y$_{2}$ (Y= As, Sb, and Bi) can be obtained if the phosphorus atoms in the α- and β-C$_{2}$P$_{2}$ replaced by other pnictogens, respectively. If the C atoms in the α- and β-C$_{2}$Y$_{2}$ (Y= P, As, Sb, and Bi) are further replaced by other IV elements X (X=Si, Ge, Sn, and Pb), respectively, more derivatives of α- and β-X$_{2}$Y$_{2}$ (Y=N, P, As, Sb, and Bi) also can be obtained. It was found that the majority of them are dynamically stable. The proposed compounds range from metal to insulators depending on their constitutions. All insulated compounds can undergo a transition from insulator to metal induced by biaxial strain. Some of them can undergo a transition from indirect band gap to direct band gap. These new compounds can become candidates as photovoltaic device, thermoelectric material field as well as lamellated superconductors.

cond-mat.mtrl-sci↗

arXiv2020

Generalised uncertainty relations for angular momentum and spin in quantum geometry

We derive generalised uncertainty relations (GURs) for angular momentum and spin in the smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum, and recovers both the generalised uncertainty principle (GUP) and the extended uncertainty principle (EUP) within a single formalism. In this paper, we investigate the consequences of these results for particles with extrinsic and intrinsic angular momentum, and obtain generalisations of the canonical ${\rm so(3)}$ and ${\rm su(2)}$ algebras. We find that, although ${\rm SO(3)}$ symmetry is preserved on three-dimensional slices of an enlarged phase space, individual subcomponents of the generalised generators obey nontrivial subalgebras. These give rise to GURs for angular momentum while leaving the canonical commutation relations intact except for a simple rescaling, $\hbar \rightarrow \hbar + β$. The value of the new parameter, $β\simeq \hbar \times 10^{-61}$, is determined by the ratio of the dark energy density to the Planck density. Here, we assume the former to be of the order of the Planck length and the latter to be of the order of the de Sitter momentum $\sim \hbar\sqrtΛ$, where $Λ$ is the cosmological constant. In the smeared-space model, $\hbar$ and $β$ are interpreted as the quantisation scales for matter and geometry, respectively, and a quantum state vector is associated with the spatial background. We show that this also gives rise to a rescaled Lie algebra for generalised spin operators, together with associated subalgebras that are analogous to those for orbital angular momentum. Remarkably, consistency of the algebraic structure requires the quantum state associated with a flat background to be fermionic, with spin eigenvalues $\pm β/2$. Finally, the modified spin algebra leads to GURs for spin measurements.

gr-qc↗

arXiv2020

Weyl type $f(Q,T)$ gravity, and its cosmological implications

We consider an $f(Q,T)$ type gravity model in which the scalar non-metricity $Q_{αμν}$ of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $w_μ$. The field equations of the theory are obtained under the assumption of the vanishing of the total scalar curvature, a condition which is added into the gravitational action via a Lagrange multiplier. The gravitational field equations are obtained from a variational principle, and they explicitly depend on the scalar nonmetricity and on the Lagrange multiplier. The covariant divergence of the matter energy-momentum tensor is also determined, and it follows that the nonmetricity-matter coupling leads to the nonconservation of the energy and momentum. The energy and momentum balance equations are explicitly calculated, and the expressions of the energy source term and of the extra force are found. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of standard general relativity. We consider several cosmological models by imposing some simple functional forms of the function $f(Q,T)$, and we compare the predictions of the theory with the standard $Λ$CDM model.

gr-qc↗

arXiv2019

Finslerian geometrization of quantum mechanics in the hydrodynamical representation

We consider a Finslerian type geometrization of the non-relativistic quantum mechanics in its hydrodynamical (Madelung) formulation, by also taking into account the effects of the presence of the electromagnetic fields on the particle motion. In the Madelung representation the Schrödinger equation can be reformulated as the classical continuity and Euler equations of classical fluid mechanics in the presence of a quantum potential, representing the quantum hydrodynamical evolution equations. The equation of particle motion can then be obtained from a Lagrangian similar to its classical counterpart. After the reparametrization of the Lagrangian it turns out that the Finsler metric describing the geometric properties of quantum hydrodynamics is a Kropina metric. We present and discuss in detail the metric and the geodesic equations describing the geometric properties of the quantum motion in the presence of electromagnetic fields. As an application of the obtained formalism we consider the Zermelo navigation problem in a quantum hydrodynamical system, whose solution is given by a Kropina metric. The case of the Finsler geometrization of the quantum hydrodynamical motion of spinless particles in the absence of electromagnetic interactions is considered in detail, and the Zermelo navigation problem for this case is also discussed.

quant-ph↗

arXiv2019

Generalised uncertainty relations from superpositions of geometries

Phenomenological approaches to quantum gravity implement a minimum resolvable length-scale but do not link it to an underlying formalism describing geometric superpositions. Here, we introduce an intuitive approach in which points in the classical spatial background are delocalised, or `smeared', giving rise to an entangled superposition of geometries. The model uses additional degrees of freedom to parameterise the superposed classical backgrounds. Our formalism contains both minimum length and minimum momentum resolutions and we naturally identify the former with the Planck length. In addition, we argue that the minimum momentum is determined by the de Sitter scale, and may be identified with the effects of dark energy in the form of a cosmological constant. Within the new formalism, we obtain both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP), which may be combined to give an uncertainty relation that is symmetric in position and momentum. Crucially, our approach does not imply a significant modification of the position-momentum commutator, which remains proportional to the identity matrix. It therefore yields generalised uncertainty relations without violating the equivalence principle, in contradistinction to existing models based on nonlinear dispersion relations. Implications for cosmology and the black hole uncertainty principle correspondence are briefly discussed, and prospects for future work on the smeared-space model are outlined.

quant-ph↗

arXiv2019

$f(Q,T)$ gravity

We propose an extension of the symmetric teleparallel gravity, in which the gravitational action $L$ is given by an arbitrary function $f$ of the nonmetricity $Q$ and of the trace of the matter energy-momentum tensor $T$, so that $L=f(Q,T)$. The field equations of the theory are obtained by varying the gravitational action with respect to both metric and connection. The covariant divergence of the field equations is obtained, with the geometry-matter coupling leading to the nonconservation of the energy-momentum tensor. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of general relativity. We consider several cosmological models by imposing some simple functional forms of the function $f(Q,T)$, corresponding to additive expressions of $f(Q,T)$ of the form $f(Q,T)=αQ+βT$, $f(Q,T)=αQ^{n+1}+βT$, and $f(Q,T)=-αQ-βT^2$. The Hubble function, the deceleration parameter, and the matter energy density are obtained as a function of the redshift by using analytical and numerical techniques. For all considered cases the Universe experiences an accelerating expansion, ending with a de Sitter type evolution. The theoretical predictions are also compared with the results of the standard $Λ$CDM model.

gr-qc↗

arXiv2019

Energy-dependent noncommutative quantum mechanics

We propose a model of dynamical noncommutative quantum mechanics in which the noncommutative strengths, describing the properties of the commutation relations of the coordinate and momenta, respectively, are arbitrary energy dependent functions. The Schrödinger equation in the energy dependent noncommutative algebra is derived for a two dimensional system for an arbitrary potential. The resulting equation reduces in the small energy limit to the standard quantum mechanical one, while for large energies the effects of the noncommutativity become important. We investigate in detail three cases, in which the noncommutative strengths are determined by an independent energy scale, related to the vacuum quantum fluctuations, by the particle energy, and by a quantum operator representation, respectively. Specifically, in our study we assume an arbitrary power law energy-dependence of the noncommutative strength parameters, and of their algebra. In this case, in the quantum operator representation, the Schrödinger equation can be formulated mathematically as a fractional differential equation. For all our three models we analyze the quantum evolution of the free particle, and of the harmonic oscillator, respectively. The general solutions of the noncommutative Schrödinger equation as well as the expressions of the energy levels are explicitly obtained.

quant-ph↗

arXiv2018

Loop Quantum Cosmology with a noncommutative quantum deformed photon gas

The noncommutativity of the space-time had important implications for the very early Universe, when its size was of the order of the Planck length. An important implication of this effect is the deformation of the standard dispersion relation of special relativity. Moreover, in the Planck regime gravity itself must be described by a quantum theory. We consider the implications of the modified dispersion relations for a photon gas, filling the early Universe, in the framework of Loop Quantum Cosmology, a theoretical approach to quantum gravity. We consider three types of deformations of the dispersion relations of the photon gas, from which we obtain the Planck scale corrections to the energy density and pressure. The cosmological implications of the modified equations of state are explored in detail for all radiation models in the framework of the modified Friedmann equation of Loop Quantum Cosmology. By numerically integrating the evolution equations we investigate the evolution of the basic cosmological parameters (scale factor, Hubble function, radiation temperature, and deceleration parameter) for a deformed photon gas filled Universe. In all models the evolution of the Universe shows the presence of a (nonsingular) bounce, corresponding to the transition from a contracting to an expanding phase.

gr-qc↗

arXiv2018

Theory of field emission

A serious barrier impedes the comparison between the theoretical prediction and the experimental observation in field emission because there is no way to measure the emission area. We introduce three dimensionless variables $\mathcal{R}_{J}$, $\mathcal{S}$ and $\mathcal{D}$ to construct a formulation for connecting directly the theoretical variables and experimental data without measuring the emission area. Based on this formulation we can analyze that the behaviors of $\mathcal{R}_{J}$ $\mathcal{S}$ and $\mathcal{D}$ with the voltages between the anode and the emitter to reveals the characteristics of current-voltage (I-V) curve and detect the physical properties of emitters. This formulation provides a way to understand the fundamental physics of I-V curve in field emission and to set up a map between the physical properties of emitters and the experimental I-V curve.

cond-mat.mtrl-sci↗

arXiv2018

Palatini formulation of $f(R,T)$ gravity theory, and its cosmological implications

We consider the Palatini formulation of $f(R,T)$ gravity theory, in which a nonminimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similarly to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra-force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the $f(R,T)$ gravity in the Palatini formulation. Cosmological models with Lagrangians of the type $f=R-α^2/R+g(T)$ and $f=R+α^2R^2+g(T)$ are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.

gr-qc↗

arXiv2018

Slowly rotating Bose Einstein Condensate galactic dark matter halos, and their rotation curves

If dark matter is composed of massive bosons, a Bose-Einstein Condensation process must have occurred during the cosmological evolution. Therefore galactic dark matter may be in a form of a condensate, characterized by a strong self-interaction. We consider the effects of rotation on the Bose-Einstein Condensate dark matter halos, and we investigate how rotation might influence their astrophysical properties. In order to describe the condensate we use the Gross-Pitaevskii equation, and the Thomas-Fermi approximation, which predicts a polytropic equation of state with polytropic index $n=1$. By assuming a rigid body rotation for the halo, with the use of the hydrodynamic representation of the Gross-Pitaevskii equation we obtain the basic equation describing the density distribution of the rotating condensate. We obtain the general solutions for the condensed dark matter density, and we derive the general representations for the mass distribution, boundary (radius), potential energy, velocity dispersion, tangential velocity and for the logarithmic density and velocity slopes, respectively. Explicit expressions for the radius, mass, and tangential velocity are obtained in the first order of approximation, under the assumption of slow rotation. In order to compare our results with the observations we fit the theoretical expressions of the tangential velocity of massive test particles moving in rotating Bose-Einstein Condensate dark halos with the data of 12 dwarf galaxies, and the Milky Way, respectively.

gr-qc↗

arXiv2017

Stabilities and novel electronic structures of three carbon nitride bilayers

Three new novel phases of carbon nitride (CN) bilayer, which are named as α-C$_{2}$N$_{2}$, β-C$_{2}$N$_{2}$ and γ-C$_{4}$N$_{4}$, respectively, have been predicted in this paper. All of them are consisted of two CN sheets connected by C-C covalent bonds. The phonon dispersions reveal that all these phases are dynamically stable, since no imaginary frequency is found for them. Transition path way between α-C$_{2}$N$_{2}$ and β-C$_{2}$N$_{2}$ is investigated, which involves bond-breaking and bond-reforming between C and N. This conversion is difficult, since the activation energy barrier is found to be 1.90 eV per unit cell, high enough to prevent the transformation at room temperature. Electronic structures calculations show that they are all semiconductors with indirect band gap of 3.76 / 5.22 eV, 4.23 / 5.75 eV and 2.06 / 3.53 eV by PBE / HSE calculation, respectively. The β-C$_{2}$N$_{2}$ has the widest band gap among the three phases. From our results, the three new two-dimensional materials have potential applications in the electronics, semiconductors, optics and spintronics.

cond-mat.mtrl-sci↗

arXiv2017

Irreversible thermodynamic description of dark matter and radiation creation during inflationary reheating

We investigate the matter creation processes during the reheating period at the end of inflation in the early Universe, by using the irreversible thermodynamic of open systems. The matter content of the Universe is assumed to consist of the inflationary scalar field, which, through its decay, generates relativistic matter, and pressureless dark matter, respectively. At the early stages of reheating the inflationary scalar field transfers its energy to the newly created matter particles, with the field energy decreasing to near zero. The general equations governing the irreversible matter creation during reheating are obtained by combining the thermodynamics description of the matter creation and the gravitational field equations. A dimensionless form of the general system of the reheating equations is also introduced. The role of the different inflationary scalar field potentials is analyzed by using analytical and numerical methods, and the evolution of the matter and scalar field densities, as well as of the cosmological parameters during reheating, are obtained. Typically, the values of the energy densities of relativistic matter and dark matter reach their maximum when the Universe is reheated up to the reheating temperature, which is determined for each case, as a function of the scalar field decay width, the scalar field particle mass, and of the cosmological parameters. An interesting result is that particle production leads to the acceleration of the Universe during the reheating phase, with the deceleration parameter showing a complex dynamics. Once the energy density of the scalar field becomes negligible with respect to the matter densities, the expansion of the Universe decelerates, and inflation has a graceful exit after reheating.

gr-qc↗

arXiv2017

Electronic Structure and Band Gap Engineering of Two-Dimensional Octagon-Nitrogene

We have predicted a new phase of nitrogen with octagon structure in our previous study, which we referred to as octa-nitrogene (ON). In this work, we make further investigation on its electronic structure. The phonon band structure has no imaginary phonon modes, which indicates that ON is dynamically stable. Using ab initio molecular dynamic simulations, the structure is found to stable up to 100K, and ripples that are similar to that of graphene is formed on the ON sheet. Based on DFT calculation on its band structure, single layer ON is a 2D large-gap semiconductor with a band gap of 4.7eV. Because of inter-layer interaction, stackings can decrease the band gap. Biaxial tensile strain and perpendicular electric field can greatly influence the band structure of ON, in which the gap decreases and eventually closes as the biaxial tensile strain or the perpendicular electric field increases. In other words, both biaxial tensile strain and perpendicular electric field can drive the insulator-to-metal transition, and thus can be used to engineer the band gap of ON. From our results, ON has potential applications in the electronics, semiconductors, optics and spintronics, and so on.

cond-mat.mtrl-sci↗

arXiv2017

A nanoscale window for probing Planck scale phenomena

The noncommutative space provides a framework to understand phenomena in Planck scale physics. However, there is no any direct experimental evidence to demonstrate the existence of noncommutative space. We propose an experimental scheme based on the Aharonov-Bohm effect in the nano-scale quantum mechanics to probe the phenomena in the noncommutative phase space. By the Seiberg-Witten map, the free electrons of the nano-scale ring in noncommutative phase space can be mapped equivalently to the quantum mechanical (Heisenberg's algebra) phase space with an extra effective magnetic flux. We introduce two variables related to the persistent current in the ring to probe the noncommutative phase space effect. We give a value-independent criterion to detect the existence of the noncommutative phase space. Namely the answer for existence or nonexistence of the noncommutative phase space depends only on the trend of the curves, rather than the values of the observation data. It can be expected to catch the noncommutative phase-space effect by this scheme.

quant-ph↗

arXiv2016

Quantum Cosmology of $f(R,T)$ gravity

Modified gravity theories have the potential of explaining the recent acceleration of the Universe without resorting to the mysterious concept of dark energy. In particular, it has been pointed out that matter-geometry coupling may be responsible for the recent cosmological dynamics of the Universe, and matter itself may play a more fundamental role in the description of the gravitational processes that usually assumed. We study the quantum cosmology of the $f(R,T)$ gravity theory, in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, and the trace of the matter energy-momentum tensor, respectively. For the background geometry we adopt the Friedmann--Robertson--Walker metric, and we assume that matter content of the Universe consists of a perfect fluid. We obtain the general form of the gravitational Hamiltonian, of the quantum potential, and of the canonical momenta, respectively. This allows us to formulate the full Wheeler-de Witt equation describing the quantum properties of this modified gravity model. As a specific application we consider in detail the quantum cosmology of the $f(R,T)=F^0(R)+θRT$ model, in which $F^0(R)$ is an arbitrary function of the Ricci scalar, and $θ$ is a function of the scale factor only. The Hamiltonian form of the equations of motion, and the Wheeler-de Witt equations are obtained, and a time parameter for the corresponding dynamical system is identified, which allows to formulate the Schrödinger--Wheeler--de Witt equation for the quantum-mechanical description of the model under consideration. A perturbative approach for the study of this equation is developed, and the energy levels of the Universe are obtained by using a twofold degenerate perturbation approach. A second quantization approach for the description of quantum time is also proposed, and briefly discussed.

gr-qc↗