arXiv subjects

Qing-hai Wang

Publications and source records attributed to Qing-hai Wang.

At least 37 records · Page 2Linked to original sources

arXiv2018

Piecewise Adiabatic Following: General Analysis and Exactly Solvable Models

The dynamics of a periodically driven system whose time evolution is governed by the Schrödinger equation with non-Hermitian Hamiltonians can be perfectly stable. This finding was only obtained very recently and will be enhanced by many exact solutions discovered in this work. The main concern of this study is to investigate the adiabatic following dynamics in such non-Hermitian systems stabilized by periodic driving. We focus on the peculiar behaviour of stable cyclic (Floquet) states in the slow-driving limit. It is found that the stable cyclic states can either behave as intuitively expected by following instantaneous eigenstates, or exhibit piecewise adiabatic following by sudden-switching between instantaneous eigenstates. We aim to cover broad categories of non-Hermitian systems under a variety of different driving scenarios. We systematically analyse the sudden-switch behaviour by a universal route. That is, the sign change of the critical exponent in our asymptotic analysis of the solutions is always found to be the underlying mechanism to determine if the adiabatic following dynamics is trivial or piecewise. This work thus considerably extends our early study on the same topic [Gong and Wang, Phys. Rev. A 97, 052126 (2018)] and shall motivate more interests in non-Hermitian systems.

quant-ph↗

arXiv2018

Field equations and particle motion in covariant emergent gravity

We derive the full set of field equations based on Hossenfelder's recent covariant formulation of the emergent gravity model, along with perturbative and exact solutions. The exact solution describes a static, spherically-symmetric spacetime with a non-trivial vector field which plays the role of dark matter under the emergent gravity paradigm. Equations of motion of relativistic test masses are derived and are shown to reduce to Modified Newtonian Dynamics with additional relativistic corrections. It is also shown that the presence of the vector field gives an additional positive contribution to the bending angle in the deflection of light.

gr-qc↗

arXiv2018

Differential geometry of time-dependent $\mathcal{PT}$-symmetric quantum mechanics

Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of time-dependent $\mathcal{PT}$-symmetric quantum mechanics. We not only find a geometric phase factor emerging naturally from cyclic evolutions of $\mathcal{PT}$-symmetric systems, but also formulate a series of differential geometry concepts, including connection, curvature, parallel transport, metric tensor, and quantum geometric tensor. Our findings constitute a useful, perhaps indispensible, tool to tackle physical problems involving $\mathcal{PT}$-symmetric systems with time-varying system's parameters. To exemplify the application of our findings, we show that the unconventional geometrical phase [Phys. Rev. Lett. 91, 187902 (2003)], consisting of a geometric phase and a dynamical phase proportional to the geometric phase, can be expressed as a single geometric phase identified in this work.

quant-ph↗

arXiv2018

Quantum Geometric Tensor in $\mathcal{PT}$-Symmetric Quantum Mechanics

A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on system's parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $\mathcal{PT}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, i.e., the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $\mathcal{PT}$-symmetry breaking in $\mathcal{PT}$-symmetric systems.

quant-ph↗

arXiv2018

The physics of large-scale food crises

Investigating the ``physics'' of food crises consists in identifying features which are common to all large-scale food crises. One element which stands out is the fact that during a food crisis there is not only a surge in deaths but also a correlative temporary decline in conceptions and subsequent births. As a matter of fact, birth reduction may even start several months before the death surge and can therefore serve as an early warning signal of an impending crisis. This scenario is studied in three cases of large-scale food crises. Finland (1868), India (1867--1907), China (1960--1961). It turns out that between the regional amplitudes of death spikes and birth troughs there is a power law relationship. This confirms what was already observed for the epidemic of 1918 in the United States (Richmond et al. 2018b). In a second part of the paper we explain how this relationship can be used for the investigation of mass-mortality episodes in cases where direct death data are either uncertain or nonexistent.

physics.bio-ph↗

arXiv2018

Piecewise Adiabatic Following in Non-Hermitian Cycling

The time evolution of periodically driven non-Hermitian systems is in general non-unitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be a genuine critical behavior and the precise phase boundary in the parameter space is located. Interestingly, the critical boundary for piecewise adiabatic following is found to be unrelated to the domain for exceptional points. To characterize the adiabatic following dynamics, we also advocate a simple definition of the Aharonov-Anandan (AA) phase for non-unitary cyclic dynamics, which always yields real AA phases. In the slow driving limit, the AA phase reduces to the Berry phase if adiabatic following persists throughout the driving without hopping, but oscillates violently and does not approach any limit in cases of piecewise adiabatic following. This work exposes the rich features of non-unitary dynamics in cases of slow cycling and should stimulate future applications of non-unitary dynamics.

quant-ph↗

arXiv2018

Criteria of existence for bounce solutions in false vacuum decay with gravity

The bounce solutions of self-interacting scalar fields coupled to gravity are studied using a semi-classical approach. We found that bounce solutions have a maximum required barrier curvature, in addition to the known minimum required barrier curvature. In particular, as the maximum barrier curvature is approached, the scale factor of the well-known Colemen-De Luccia (CDL) bounce solutions become divergent. Unlike the CDL or its more general oscillating bounce counterparts, this cannot be considered as a subset of the Hawking-Turok solution.

gr-qc↗

arXiv2017

Dynamical quantum phase transitions in non-Hermitian lattices

In closed quantum systems, a dynamical phase transition is identified by nonanalytic behaviors of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a non-Hermitian lattice realized by optical resonators. Dynamical quantum phase transitions with topological signatures are found when an isolated exceptional point is crossed during the quench. A topological winding number defined by a real, noncyclic geometric phase is introduced, whose value features quantized jumps at critical times of these phase transitions and remains constant elsewhere, mimicking the plateau transitions in quantum Hall effects. This work provides a simple framework to study dynamical and topological responses in non-Hermitian systems.

cond-mat.stat-mech↗

arXiv2017

Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime

An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the exact solution, we obtain a small bending-angle-approximation for a lens system where the source, lens and observer are co-aligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to non-existent null trajectories. The linear coefficient $γ$ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by General Relativity for small $γ$.

gr-qc↗

arXiv2014

Stabilizing Non-Hermitian Systems by Periodic Driving

The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet operator may become all real. This possibility can emerge for a continuous range of system parameters with subtle domain boundaries. It is further shown that the issue of stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of lattice Hamiltonians. As an application, we show how to use the stability of driven non-Hermitian two-level systems (0-dimension in space) to simulate a spectrum analogous to Hofstadter's butterfly that has played a paradigmatic role in quantum Hall physics. The simulation of the band structure of non-Hermitian superlattice potentials with parity-time reversal symmetry is also briefly discussed.

quant-ph↗

arXiv2013

Boosting work characteristics and overall heat engine performance via shortcuts to adiabaticity: quantum and classical systems

Under a general framework, shortcuts to adiabatic processes are shown to be possible in classical systems. We then study the distribution function of the work done on a small system initially prepared at thermal equilibrium. It is found that the work fluctuations can be significantly reduced via shortcuts to adiabatic processes. For example, in the classical case probabilities of having very large or almost zero work values are suppressed. In the quantum case negative work may be totally removed from the otherwise non-positive-definite work values. We also apply our findings to a micro Otto-cycle-based heat engine. It is shown that the use of shortcuts, which directly enhances the engine output power, can also increase the heat engine efficiency substantially, in both quantum and classical regimes.

quant-ph↗

arXiv2013

Time Dependent $\mathcal{PT}$-Symmetric Quantum Mechanics

The parity-time-reversal- ($\mathcal{PT}$) symmetric quantum mechanics (PTQM) has developed into a noteworthy area of research. However, to date most known studies of PTQM focused on the spectral properties of non-Hermitian Hamiltonian operators. In this work, we propose an axiom in PTQM in order to study general time-dependent problems in PTQM, e.g., those with a time-dependent $\mathcal{PT}$-symmetric Hamiltonian and with a time-dependent metric. We illuminate our proposal by examining a proper mapping from a time-dependent Schrödinger-like equation of motion for PTQM to the familiar time-dependent Schrödinger equation in conventional quantum mechanics. The rich structure of the proper mapping hints that time-dependent PTQM can be a fruitful extension of conventional quantum mechanics. Under our proposed framework, we further study in detail the Berry phase generation in a class of $\mathcal{PT}$-symmetric two-level systems. It is found that a closed path in the parameter space of PTQM is often associated with an open path in a properly mapped problem in conventional quantum mechanics. In one interesting case we further interpret the Berry phase as the flux of a continuously tunable fictitious magnetic monopole, thus highlighting the difference between PTQM and conventional quantum mechanics despite the existence of a proper mapping between them.

quant-ph↗

arXiv2013

Speeding Up Classical and Quantum Adiabatic Processes: Implications for Work Functions and Heat Engine Designs

Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. We speed up both classical and quantum adiabatic processes by adding control protocols. In classical systems, we work out the control protocols by analyzing the classical adiabatic approximation. In quantum systems, we follow the idea of transitionless driving by Berry [J. Phys. A: Math. Theor. Vol.42 365303 (2009)]. Such fast-forward adiabatic processes can be performed at arbitrary fast speed, and in the meanwhile reduce the work fluctuation. In both systems, we use a time-dependent harmonic oscillator model to work out explicitly the work function and the work fluctuation in three types of processes: fast-forward adiabatic processes, adiabatic processes, and non-adiabatic processes. We show the significant reduction on work fluctuation in fast-forward adiabatic process. We further illustrate how the fast-forward process improved the converging rate of the Jarzynski equality between the work function and the free energy. As an application, we show that the fast-forward process not only maximizes the output power but also improve the efficiency of a quantum engine.

quant-ph↗

arXiv2012

General PT-Symmetric Matrices

Three ways of constructing a non-Hermitian matrix with possible all real eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and generalized PT symmetry. Parameter counting is provided for each class. All three classes of matrices have more real parameters than a Hermitian matrix with the same dimension. The generalized PT-symmetric matrices are most general among the three. All self-adjoint matrices process a generalized PT symmetry. For a given matrix, it can be both PT-symmetric and P'-pseudo-Hermitian with respect to some P' operators. The relation between corresponding P and P' operators is established. The Jordan block structures of each class are discussed. Explicit examples in 2x2 are shown.

quant-ph↗

arXiv2012

Entanglement Efficiencies in PT-Symmetric Quantum Mechanics

The degree of entanglement is determined for an arbitrary state of a broad class of PT-symmetric bipartite composite systems. Subsequently we quantify the rate with which entangled states are generated and show that this rate can be characterized by a small set of parameters. These relations allow one in principle to improve the ability of these systems to entangle states. It is also noticed that many relations resemble corresponding ones in conventional quantum mechanics.

hep-th↗

arXiv2012

2*2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices

A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or parity-time- (PT-) symmetric matrices. To illustrate the main idea, we first study 2*2 complex Hermitian matrix ensembles with O(2) invariant constraints, yielding novel level-spacing statistics such as singular distributions, half-Gaussian distribution, distributions interpolating between GOE (Gaussian Orthogonal Ensemble) distribution and half Gaussian distributions, as well as gapped-GOE distribution. Such a symmetry-reduction strategy is then used to explore 2*2 PT-symmetric matrix ensembles with real eigenvalues. In particular, PT-symmetric random matrix ensembles with U(2) invariance can be constructed, with the conventional complex Hermitian random matrix ensemble being a special case. In two examples of PT-symmetric random matrix ensembles, the level-spacing distributions are found to be the standard GUE (Gaussian Unitary Ensemble) statistics or "truncated-GUE" statistics.

quant-ph↗

arXiv2010

PT Symmetry as a Generalization of Hermiticity

The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear vector space with a dynamic inner product. The most general PT-symmetric matrix Hamiltonians are constructed for 2*2 and 3*3 cases. In the former case, the PT-symmetric Hamiltonian represents the most general matrix Hamiltonian with a real spectrum. In both cases, Hermitian matrices are shown to be special cases of PT-symmetric matrices. This finding confirms and strengthens the early belief that the PT-symmetric quantum mechanics is a generalization of the conventional Hermitian quantum mechanics.

quant-ph↗

arXiv2010

Geometric Phase in PT-Symmetric Quantum Mechanics

Unitary evolution in PT-symmetric quantum mechanics with a time-dependent metric is found to yield a new class of adiabatic processes. As an explicit example, a Berry-like phase associated with a PT-symmetric two-level system is derived and interpreted as the flux of a fictitious monopole with a tunable charge plus a singular string component with non-trivial phase contributions. The Hermitian analog of our results is also discussed.

quant-ph↗