Time-reversal Systems Research Articles

Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry (1985) within the so-called diagonal approximation of semiclassical periodic-orbit sums. Derivation of the full RMT spectral form factor $K(t)$ from semiclassics has been completed only much later in a tour de force by Mueller et al (2004). In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming at the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed as `many-body localized phase' and `ergodic phase'. In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide the first theoretical explanation for these observations. We compute $K(t)$ explicitly in the leading two orders in $t$ and show its agreement with RMT for non-integrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin 1/2 models in a periodically kicking transverse field.

High Resolution Carrier Frequency Offset Estimation in Time-Reversal Wideband Communications

Time-reversal (TR) wideband communication systems enjoy the spatial–temporal focusing effect in a rich-scattering environment. However, the performance degrades in the presence of carrier frequency offset (CFO). The impact of CFO can be mitigated by compensating the estimated CFO values obtained using CFO estimators. Yet, CFO estimators in literature cannot work well in wideband TR systems due to the fact that the normalized CFO values are very small and thus cannot be estimated accurately using conventional schemes. To address this issue, we propose four CFO estimators which are capable of accurate CFO estimations for wideband TR systems. The theoretical performances of the proposed estimators are analyzed. Additionally, realizing that phase wrapping might introduce severe bias into CFO estimations, we present the conditions on the system parameters so that phase wrapping can be avoided. Extensive simulations and experimental results demonstrate the superiority of the proposed methods.

Evanescent-Wave Reconstruction in Time Reversal System

AbstractThe evanescent wave re-construction performance in the time reversal system with periodic sub-wavelength grating is studied in this paper. Both the analysis and calculation results show that the evanescent components of the initial wave can’t be re-constructed directly by far field time reversal processing. The results indicate the uncertainty of the super-resolution performance of the time reversal technique with randomly arranged scatters. A new method to achieve super-resolution imaging by using evanescent-to-propagation wave conversion also been proposed at the end of this paper.

Path-integral Monte Carlo simulation of time-reversal noninvariant bulk systems with a case study of rotating Yukawa gases.

We elaborate on the methodology to simulate bulk systems in the absence of time-reversal symmetry by the phase-fixed path-integral Monte Carlo method under (possibly twisted) periodic boundary conditions. Such systems include two-dimensional electrons in the quantum Hall regime and rotating ultracold Bose and Fermi gases; time-reversal symmetry is broken by an external magnetic field and the Coriolis force, respectively. We provide closed-form expressions in terms of Jacobi elliptic functions for the thermal density matrix (or the Euclidean propagator) of a single particle on a flat torus under very general conditions. We then modify the multislice sampling method in order to sample paths by the magnitude of the complex-valued thermal density matrix. Finally, we demonstrate that these inventions let us study the vortex melting process of a two-dimensional Yukawa gas in terms of the de Boer interaction strength parameter, temperature, and rotation (Coriolis force). The bosonic case is relevant to ultracold Fermi-Fermi mixtures of widely different masses under rotation.

A Time-Reversal Imaging System for Breast Screening: Theory and Initial Phantom Results.

In this paper, a working ultrawideband (UWB) microwave imaging (MI) system using basic techniques is proposed to detect and localize a tumor model. The system harnesses the time reversal-decomposition of time reversal operator (DORT) signal processing method. We suggest a modified background Green's function and suitable spiral antennas for time reversal imaging of a breast cancer tumor. In this method, scatterings from a breast phantom are measured. Then, reflected signals are processed using the decomposition of time reversal (TR), known under French acronym DORT, algorithm. In a conventional TR imaging method, free-space Green's function is used for detection. However, in the present method, we employ cylindrical Green's functions of a two-layer medium. This makes a better model of the background medium for TR-DORT imaging. Also, the performance of TR-DORT detector against signal to clutter ratio, and its ability to detect and localize different shapes, sizes, and permittivity values of breast tumor are discussed. Furthermore, a fatty tissue phantom model is used to verify the results experimentally. The MI system is tested to localize a tumor within the breast Debye phantom at the frequency range of 3.1-10.6GHz. The experimental results show the validity of our proposed system.

Classical reconstruction of interference patterns of position-wave-vector–entangled photon pairs by the time-reversal method

The quantum interference of entangled photons forms a key phenomenon underlying various quantum-optical technologies. It is known that the quantum interference patterns of entangled photon pairs can be reconstructed classically by the time-reversal method; however, the time-reversal method has been applied only to time-frequency-entangled two-photon systems in previous experiments. Here, for the first time, we apply the time-reversal method to the position-wavevector-entangled two-photon systems: the two-photon Young interferometer and the two-photon beam focusing system. We experimentally demonstrate that the time-reversed systems classically reconstruct the same interference patterns as the position-wavevector-entangled two-photon systems.

Theory of superconductivity with non-Hermitian and parity-time reversal symmetric Cooper pairing symmetry

Recently developed parity (P) and time-reversal (T) symmetric non-Hermitian systems govern a rich variety of new and characteristically distinct physical properties, which may or may not have a direct analog in their Hermitian counterparts. We study here a non-Hermitian, PT-symmetric superconducting Hamiltonian that possesses real quasiparticle spectrum in the PT-region of the Brillouin zone. Within a single-band mean-field theory, we find that real quasiparticle energies are possible when the superconducting order parameter itself is either Hermitian or anti-Hermitian. Within the corresponding Bardeen-Cooper-Schrieffer (BCS) theory, we find that several properties are characteristically distinct and novel in the non-Hermitian pairing case than its Hermitian counterpart. One of our significant findings is that while a Hermitian superconductor gives a second order phase transition, the non-Hermitian one produces a robust first order phase transition. The corresponding thermodynamic properties, and the Meissner effect are also modified accordingly. Finally, we discuss how such a PT-symmetric pairings can emerge from an anti-symmetric potential, such as the Dzyloshinskii-Moria interaction, but with an external external bath, or complex potential, among others.

Reversing the irreversible: From limit cycles to emergent time symmetry

In 1979 Penrose hypothesized that the arrows of time are explained by the hypothesis that the fundamental laws are time irreversible. That is, our reversible laws, such as the standard model and general relativity are effective, and emerge from an underlying fundamental theory which is time irreversible. In Cort\^{e}s and Smolin (2014a, 2014b, 2016) we put forward a research program aiming at realizing just this. The aim is to find a fundamental description of physics above the planck scale, based on irreversible laws, from which will emerge the apparently reversible dynamics we observe on intermediate scales. Here we continue that program and note that a class of discrete dynamical systems are known to exhibit this very property: they have an underlying discrete irreversible evolution, but in the long term exhibit the properties of a time reversible system, in the form of limit cycles. We connect this to our original model proposal in Cort\^{e}s and Smolin (2014a), and show that the behaviours obtained there can be explained in terms of the same phenomenon: the attraction of the system to a basin of limit cycles, where the dynamics appears to be time reversible. Further than that, we show that our original models exhibit the very same feature: the emergence of quasi-particle excitations obtained in the earlier work in the space-time description is an expression of the system's convergence to limit cycles when seen in the causal set description.

A Fine-Grained Analysis of Time Reversal MU-MISO Systems Over Correlated Multipath Channels With Imperfect CSI

Time reversal (TR) is regarded as a potential future transmission scheme for multi-user (MU) multiple-input single-output (MISO) ultra-wideband (UWB) communication systems. In spite of TR’s good performance in MU-MISO UWB systems, it suffers from performance degradation due to spatial correlation and imperfect channel-state information. In this paper, a comprehensive performance analysis of MU-MISO UWB systems with a TR pre-filter is provided. Both spatial correlation and channel estimation errors (CEE) are taken into account in the propagation channel model, and the system performance is mainly studied in terms of its effective signal-to-interference-plus-noise ratio (SINR), channel capacity, and bit error rate. The novel closed-form expressions for the average effective SINR are derived in order to characterize the influence of propagation conditions such as channel impulse response duration, spatial correlation, and CEE on TR performance metrics. The expressions reveal more precisely to us that spatial correlation and CEE have different effects on the average power of the desired signal, inter-symbol interference, and inter-user interference. Moreover, the impacts of spatial correlation and CEE on the performance of MU-MISO TR system are thoroughly investigated. In particular, the capacity loss of MU-MISO TR system due to spatial correlation and CEE is quantified and fully discussed at the end of this paper. It is shown that high spatial correlation and CEE cause a remarkable reduction in bandwidth efficiency. Finally, all theoretical results are confirmed by numerical simulations.

Performance Comparison with Different Antenna Properties in Time Reversal Ultra-Wideband Communications for Sensor System Applications.

The complexity reduction of receivers in ultrawideband (UWB) communication when time reversal (TR) technique is applied makes it suitable for low-cost and low-power sensor systems. Larger antenna dispersion can generally lead to a less stable phase center and will increase the interference in UWB communications based on pulse radio, whereas a higher antenna gain will result in higher channel gain and further larger channel capacity. To find out the trade-off between antenna gain and dispersion, we performed the channel measurements using different antennas in a dense multipath environment and established the distribution of channel capacities based on the measured channel responses. The results show that the capacity loss caused by antenna dispersion cannot be compensated by antenna gain with line-of-sight transmission to some extent, the effect of phase center on the communication system is negligible, and antennas with smaller time dispersion will have a better energy focusing property and anti-interference performance in TR systems.

Information Landscape and Flux, Mutual Information Rate Decomposition and Connections to Entropy Production

We explored the dynamics of two interacting information systems. We show that for the Markovian marginal systems, the driving force for information dynamics is determined by both the information landscape and information flux. While the information landscape can be used to construct the driving force to describe the equilibrium time-reversible information system dynamics, the information flux can be used to describe the nonequilibrium time-irreversible behaviors of the information system dynamics. The information flux explicitly breaks the detailed balance and is a direct measure of the degree of the nonequilibrium or time-irreversibility. We further demonstrate that the mutual information rate between the two subsystems can be decomposed into the equilibrium time-reversible and nonequilibrium time-irreversible parts, respectively. This decomposition of the Mutual Information Rate (MIR) corresponds to the information landscape-flux decomposition explicitly when the two subsystems behave as Markov chains. Finally, we uncover the intimate relationship between the nonequilibrium thermodynamics in terms of the entropy production rates and the time-irreversible part of the mutual information rate. We found that this relationship and MIR decomposition still hold for the more general stationary and ergodic cases. We demonstrate the above features with two examples of the bivariate Markov chains.

Nature of continuous phase transitions in interacting topological insulators

We revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidences for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that, the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Partial local density of states from scanning gate microscopy

Scanning gate microscopy images from measurements made in the vicinity of quantum point contacts were originally interpreted in terms of current flow. Some recent work has analytically connected the local density of states to conductance changes in cases of perfect transmission, and at least qualitatively for a broader range of circumstances. In the present paper, we show analytically that in any time-reversal invariant system there are important deviations that are highly sensitive to imperfect transmission. Nevertheless, the unperturbed partial local density of states can be extracted from a weakly invasive scanning gate microscopy experiment, provided the quantum point contact is tuned anywhere on a conductance plateau. A perturbative treatment in the reflection coefficient shows just how sensitive this correspondence is to the departure from the quantized conductance value and reveals the necessity of local averaging over the tip position. It is also shown that the quality of the extracted partial local density of states decreases with increasing tip radius.

Classification of accidental band crossings and emergent semimetals in two-dimensional noncentrosymmetric systems

We classify all possible gap-closing procedures which can be achieved in two-dimensional time-reversal invariant noncentrosymmetric systems. For exhaustive classification, we examine the space-group symmetries of all 49 layer groups lacking inversion, taking into account spin-orbit coupling. Although a direct transition between two insulators is generally predicted to occur when a band crossing happens at a general point in the Brillouin zone, we find that a variety of stable semimetal phases with point or line nodes can also arise due to the band crossing in the presence of additional crystalline symmetries. Through our theoretical study, we provide the complete list of nodal semimetals created by a band inversion in two-dimensional noncentrosymmetric systems with time-reversal invariance. The transition from an insulator to a nodal semimetal can be grouped into three classes depending on the crystalline symmetry. First, in systems with a twofold rotation about the $z$ axis (normal to the system), a band inversion at a generic point generates a two-dimensional Weyl semimetal with point nodes. Second, when the band crossing happens on the line invariant under a twofold rotation (mirror) symmetry with the rotation (normal) axis lying in the two-dimensional plane, a Weyl semimetal with point nodes can also be obtained. Finally, when the system has a mirror symmetry about the plane embracing the whole system, a semimetal with nodal lines can be created. Applying our theoretical framework, we identify various two-dimensional materials as candidate systems in which stable nodal semimetal phases can be induced via doping, applying electric field, or strain engineering, etc.

How to Bridge Attractors and Repellors

Strange attractors have been extensively studied, but the same is not true for strange repellors. Some time-reversible systems have repellors that mirror their corresponding attractors and that exchange roles when time is reversed. In this paper, a conversion operator is introduced by which an easy transformation can be constructed between such a time-reversible system with an attractor/repellor pair and an irreversible one with a pair of attractors, or vice versa, thus expanding the list of such examples.

Downlink MAC Scheduler for 5G Communications With Spatial Focusing Effects

Driven by the demand for supporting the rapidly increasing wireless traffic, the next-generation communication system, i.e., the 5G system, needs to accommodate a massive number of users and judiciously manage the interference. One promising candidate, the time reversal (TR) system, uses a large bandwidth and designs transmitting waveforms, such that the environment acts as a matched filter and the transmitted signal adds up coherently at the intended users. Therefore, the energy is focused only at the intended users with reduced interference to others. The other candidate, massive MIMO system, utilizes a large number of antennas to focus on the energy to the users and reduce the mutual interference. However, the massive number of users poses a limit on system performance due to increasing interuser interference, and the system has to make a judicial selection of transmitting users. In this paper, we propose a scheduler that maximizes the system weighted sum rate while satisfying the minimum rate requirements of the transmitting users. The optimization problem is transformed into a mixed integer quadratically constrained quadratic programming with linear time complexity. We also investigate the impact of imperfect channel information on the proposed scheduler algorithm and reveal similar channel estimation error distribution between the TR and massive MIMO system. We evaluate the performance of the proposed scheduler in different scenarios and the results show that the proposed scheduler has several desirable characteristics, including low time complexity, suitable on versatile system structure, and robustness against imperfect channel information.

Tomonaga-Luttinger liquid and localization in Weyl semimetals

We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each strongly correlated wire can be approached within the Tomonaga-Luttinger liquid formalism. Including impurity scatterings, we inspect the localization effect and the temperature dependence of the electrical resistivity. The effect of a large number of Weyl points in real materials is also discussed.

0−π transitions in a Josephson junction of an irradiated Weyl semimetal

We propose a setup for the experimental realization of unexpected and anisotropic $0$-$\pi$ transitions of the Josephson current, in a junction whose link is made of irradiated Weyl semi-metal (WSM), due to the presence of chiral nodes. We show using a Green's function technique that the Josephson current through a time-reversal symmetric WSM has anisotropic periodic oscillations as a function of $k_0L$, where $k_0$ is the (relevant) separation of the chiral nodes and $L$ is the length of the sample. This is unexpected, for time-reversal symmetric systems, although it has been shown earlier for time-reversal symmetry breaking WSMs. We then show that the effective value of $k_0$ can be tuned with precision by irradiating the sample with photons resulting in $0$-$\pi$ transitions of the critical current. Finally, we discuss the robustness of our setup.

On three types of dynamics and the notion of attractor

We propose a theoretical framework for explaining the numerically discovered phenomenon of the attractor–repeller merger. We identify regimes observed in dynamical systems with attractors as defined in a paper by Ruelle and show that these attractors can be of three different types. The first two types correspond to the well-known types of chaotic behavior, conservative and dissipative, while the attractors of the third type, reversible cores, provide a new type of chaos, the so-called mixed dynamics, characterized by the inseparability of dissipative and conservative regimes. We prove that every elliptic orbit of a generic non-conservative time-reversible system is a reversible core. We also prove that a generic reversible system with an elliptic orbit is universal; i.e., it displays dynamics of maximum possible richness and complexity.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry.

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z_{2} topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.