Search

We consider a Su-Schrieffer-Heeger chain to which we attach a semi-infinite undimerized chain (lead) to both ends. We study the effect of the openness of the SSH model on its properties. A representation of the infinite system using an effective Hamiltonian allows us to examine its low-energy states in more detail. We show that, as one would expect, the topological edge states hybridize as the coupling between the systems is increased. As this coupling grows, these states are suppressed, while a new type of edge state emerges from the trivial topological phase. These new states, referred to as phase-inverted edge states, are localized low-energy modes very similar to the edge states of the topological phase. Interestingly, localization occurs on a new shifted interface, moving from the first (and last) site to the second (and second to last) site. This suggests that the topology of the system is strongly affected by the leads, with three regimes of behavior. For very small coupling the system is in a well-defined topological phase; for very large coupling it is in the opposite phase; in the intermediate region, the system is in a transition regime., Comment: 14 pages, 11 figures

In this work, we propose a novel qubit-based sensor with the ability to characterize topological edge states in low-dimensional systems. A composite system is studied, consisting of a qubit coupled to a topologically nontrivial Su-Schrieffer-Heeger chain between semi-infinite lead channels. This qubit probe utilizes decoherence dynamics which, under a weak-coupling framework, are related to the environment's local density of states. Qubit decoherence rate measurements along a sample therefore provide the means to extract edge state profiles. The environment's influence on the qubit's subspace is captured by an effective projective treatment, leading to an analytical decoherence rate expression. We demonstrate that the scanning qubit probe identifies and yields a complete spatial characterization of the topological edge states within the composite system., Comment: 9 pages, 5 figures

Reconfigurable intelligent surface (RIS) is promising for future 6G wireless communications. However, the increased number of RIS elements results in the high overhead for channel acquisition and the non-negligible power consumption. Therefore, how to improve the system capacity with limited RIS elements is essential. Unlike the classical regular RIS whose elements are arranged on a regular grid, in this paper, we propose an irregular RIS structure to improve the system capacity. The key idea is to irregularly configure a given number of RIS elements on an enlarged surface, which provides extra spatial degrees of freedom compared with the regular RIS. In this way, the received signal power can be enhanced, and thus the system capacity can be improved. Then, we formulate a joint topology and precoding optimization problem to maximize the capacity for irregular RIS-aided communication systems. Accordingly, a joint optimization algorithm with low complexity is proposed to alternately optimize the RIS topology and the precoding design. Particularly, a tabu search-based method is used to design the irregular RIS topology, and a neighbor extraction-based cross-entropy method is introduced to optimize the precoding design. Simulation results demonstrate that, subject to the constraint of limited RIS elements, the proposed irregular RIS can significantly enhance the system capacity., Comment: Accepted by IEEE Transactions on Vehicular Technology. Simulation codes are provided at: http://oa.ee.tsinghua.edu.cn/dailinglong/publications/publications.html

One of the most challenging problems for the realization of a scalable quantum computer is to design a physical device that keeps the error rate for each quantum processing operation low. These errors can originate from the accuracy of quantum manipulation, such as the sweeping of a gate voltage in solid state qubits or the duration of a laser pulse in optical schemes. Errors also result from decoherence, which is often regarded as more crucial in the sense that it is inherent to the quantum system, being fundamentally a consequence of the coupling to the external environment. Grouping small collections of qubits into clusters with symmetries can protect parts of the calculation from decoherence. We use 4-level cores with a straightforward generalization of discrete rotational symmetry, omega-rotation invariance, to encode pairs of coupled qubits and universal 2-qubit logical gates. We include quantum errors as a main source of decoherence, and show that symmetry makes logical operations particularly resilient to untimely anisotropic qubit rotations. We propose a scalable scheme for universal quantum computation where cores play the role of quantum-computational transistors, quansistors. Initialization and readout are achieved by coupling to leads. The external leads are explicitly considered and are assumed to be the other main source of decoherence. We show that quansistors can be dynamically decoupled from the leads by tuning their internal parameters, giving them the versatility required to act as controllable quantum memory units. With this dynamical decoupling, logical operations within quansistors are also symmetry-protected from unbiased noise in their parameters. We identify technologies that could implement omega-rotation invariance. Many of our results can be generalized to higher-level omega-rotation-invariant systems, or adapted to clusters with other symmetries., Comment: 23 pages, 19 figures

Benefiting from the growth of the bandwidth, Terahertz (THz) communication can support the new application with explosive requirements of the ultra-high-speed rates for future 6G wireless systems. In order to compensate for the path loss of high frequency, massive multiple-input multiple-output (MIMO) can be utilized for high array gains by beamforming. However, since a large number of analog phase shifters should be used to realize the analog beamforming, the existing THz communication with massive MIMO has very high energy consumption. To solve this problem, a reconfigurable intelligent surface (RIS)-based hybrid precoding architecture for THz communication is developed in this paper, where the energy-hungry phased array is replaced by the energy-efficient RIS to realize the analog beamforming of the hybrid precoding. Then, based on the proposed RIS-based architecture, a sum-rate maximization problem for hybrid precoding is investigated. Since the phase shifts implemented by RIS in practice are often discrete, this sum-rate maximization problem with a non-convex constraint is challenging. Next, the sum-rate maximization problem is reformulated as a parallel deep neural network (DNN)-based classification problem, which can be solved by the proposed low-complexity deep learning-based multiple discrete classification (DL-MDC) hybrid precoding scheme. Finally, we provide numerous simulation results to show that the proposed DL-MDC scheme works well both in the theoretical Saleh-Valenzuela channel model and practical 3GPP channel model. Compared with existing iterative search algorithms, the can proposed DL-MDC scheme reduces the runtime significantly with a negligible performance loss., Comment: 26 pages, 7 figures

In the context of gravity in the strong-coupling regime, the propagation amplitude of gravity coupled to relativistic particles undergoing geodesic separation is calculated exactly. Geodesic separation gives rise to boundary terms associated with the h_\times and h_+ graviton components. At low temperatures the propagation amplitude vanishes, implying no graviton propagation in this regime., Comment: 7 pages

If the neutrino is a Majorana particle, low-energy lepton-number-violating (LNV) processes, such as neutrinoless double-beta ($0\nu\beta\beta$) decay, are possible. It may also be possible to observe high-energy $0\nu\beta\beta$-like LNV processes at the LHC. These are distinguished by the presence of same-sign dileptons in the final state (e.g., ${\bar u} d \to t {\bar b} \, e^- \mu^-$). In this paper, we show that CP-violating triple products (TPs) may be present in the process, and may be measurable at the LHC. If a nonzero TP were observed, it would give us much information about the underlying new physics (NP). We would know that there are (at least) two interfering NP amplitudes, with different weak phases and different Lorentz structures. And if we had some knowledge of the NP, e.g., by direct production of NP particles, we could get information about the magnitudes and relative phases of its couplings., Comment: 8 pages, 1 figure. Important changes to the paper: we now focus on a single NP model, and include a detailed discussion about the prospects for the observation of TPs at the LHC

As is well known, qubits are the fundamental building blocks of quantum computers, and more generally, of quantum information. A major challenge in the development of quantum devices arises because the information content in any quantum state is rather fragile, as no system is completely isolated from its environment. Generally, such interactions degrade the quantum state, resulting in a loss of information. Topological edge states are promising in this regard because they are in ways more robust against noise and decoherence. But creating and detecting edge states can be challenging. We describe a composite system consisting of a two-level system (the qubit) interacting with a finite Su-Schrieffer-Heeger chain (a hopping model with alternating hopping parameters) attached to an infinite chain. In this model, the dynamics of the qubit changes dramatically depending on whether or not an edge state exists. Thus, the qubit can be used to determine whether or not an edge state exists in this model., Comment: 8 pages, 5 figures. Talk given at Quantum Theory and Symmetries XI, Montreal QC, 1-5 July, 2019

We consider the Su-Schrieffer-Heeger (SSH) chain, which has 0, 1, or 2 topological edge states depending on the ratio of the hopping parameters and the parity of the chain length. We couple a qubit to one edge of the SSH chain and a semi-infinite undimerized chain to the other, and evaluate the dynamics of the qubit. By evaluating the decoherence rate of the qubit we can probe the edge states of the SSH chain. The rate shows strong even-odd oscillations with the number of sites reflecting the presence or absence of edge states. Hence, the qubit acts as an efficient detector of the topological edge states of the SSH model. This can be generalized to other topological systems., Comment: 10 pages, 9 figures

We consider the Skyrme model modified by the addition of mass terms which explicitly break chiral symmetry and pick out a specific point on the model's target space as the unique true vacuum. However, they also allow the possibility of false vacua, local minima of the potential energy. These false vacuum configurations admit metastable skyrmions, which we call false skyrmions. False skyrmions can decay due to quantum tunnelling, consequently causing the decay of the false vacuum. We compute the rate of decay of the false vacuum due to the existence of false skyrmions., Comment: 12 pages, 11 figures

We study the effect of vortices on the tunneling decay of a symmetry-breaking false vacuum in three spacetime dimensions with gravity. The scenario considered is one in which the initial state, rather than being the homogeneous false vacuum, contains false vortices. The question addressed is whether, and, if so, under which circumstances, the presence of vortices has a significant catalyzing effect on vacuum decay. After studying the existence and properties of vortices, we study their decay rate through quantum tunneling using a variety of techniques. In particular, for so-called thin-wall vortices we devise a one-parameter family of configurations allowing a quantum-mechanical calculation of tunneling. Also for thin-wall vortices, we employ the Israel junction conditions between the interior and exterior spacetimes. Matching these two spacetimes reveals a decay channel which results in an unstable, expanding vortex. We find that the tunneling exponent for vortices, which is the dominant factor in the decay rate, is half that for Coleman-de Luccia bubbles. This implies that vortices are short-lived, making them cosmologically significant even for low vortex densities. In the limit of the vanishing gravitational constant we smoothly recover our earlier results for the decay of the false vortex in a model without gravity., Comment: 27 pages, 8 figures, Typos corrected

Non-orthogonal multiple access (NOMA) is a promising technique for the fifth generation (5G) wireless communications. As users with good channel conditions can serve as relays to enhance the system performance by using successive interference cancellation (SIC), the integration of NOMA and cooperative relaying has recently attracted increasing interests. In this paper, a NOMA-based cooperative relaying system is studied, and an analytical framework is developed to evaluate its performance. Specifically, the performance of NOMA over Rician fading channels is studied, and the exact expression of the average achievable rate is derived. Moreover, we also propose an approximation method to calculate the achievable rate by using the Gauss-Chebyshev Integration. Numerical results confirm that our derived analytical results match well with the Monte Carlo simulations., Comment: 5 pages, 3 figures. To appear in IEEE Transactions on Vehicular Technology. Simulation codes are provided to reproduce the results presented in this paper: http://oa.ee.tsinghua.edu.cn/dailinglong/publications/publications.html

Anderson localization is a consequence of coherent interference of multiple scattering events in the presence of disorder, which leads to an exponential suppression of the transmission. The decay of the transmission is typically probed at a given energy or frequency. Here we show that this decay affects the dynamics of a qubit coupled to the disordered system and we express the relaxation rate of the qubit in terms of the localization properties. Conversely, adding static disorder to a channel coupled to a qubit will reduce the decoherence rate of the qubit. Hence, when designing electrodes that couple to qubits it is possible to improve their performance by adding impurities to the channel., Comment: 12 pages, 8 figures

We study the decay of "false" domain walls, which are metastable states of the quantum theory where the true vacuum is trapped inside the wall, with the false vacuum outside. We consider a theory with two scalar fields, a shepherd field and a field of sheep. The shepherd field serves to herd the solitons of the sheep field so that they are nicely bunched together. However, quantum tunnelling of the shepherd field releases the sheep to spread out uncontrollably. We show how to calculate the tunnelling amplitude for such a disintegration., Comment: 20 pages, 9 figures

We consider the decay of "false kinks," that is, kinks formed in a scalar field theory with a pair of degenerate symmetry-breaking false vacua in 1+1 dimensions. The true vacuum is symmetric. A second scalar field and a peculiar potential are added in order for the kink to be classically stable. We find an expression for the decay rate of a false kink. As with any tunneling event, the rate is proportional to $\exp(-S_E)$ where $S_E$ is the Euclidean action of the bounce describing the tunneling event. This factor varies wildly depending on the parameters of the model. Of interest is the fact that for certain parameters $S_E$ can get arbitrarily small, implying that the kink is only barely stable. Thus, while the false vacuum itself may be very long-lived, the presence of kinks can give rise to rapid vacuum decay., Comment: 21 pages, 13 figures

The interplay between the various measures of quantum correlations are well known in stable optical and electronic systems. Here, for the first time, we study such foundational issues in unstable quantum systems. Specifically we study meson-antimeson systems, which are produced copiously in meson factories. We use the semigroup formalism to compute the time evolution of several measures of quantum correlations for three meson systems (K-Kbar, Bd-Bdbar and Bs-Bsbar), circumventing difficulties which arise using other methods due to the instability of these particles. We then compare these measures to one another and find that the relations between them can be nontrivially different from those of their stable counterparts such as neutrinos., Comment: 6 pages, one figure

We consider the decay of cosmic strings that are trapped in the false vacuum in a theory of scalar electrodynamics in 3+1 dimensions. We restrict our analysis to the case of thin-walled cosmic strings which occur when large magnetic flux trapped inside the string. Thus the string looks like a tube of fixed radius, at which it is classically stable. The core of the string contains magnetic flux in the true vacuum, while outside the string, separated by a thin wall, is the false vacuum. The string decays by tunnelling to a configuration which is represented by a bulge, where the region of true vacuum within, is ostensibly enlarged. The bulge can be described as the meeting, of a kink soliton anti-soliton pair, along the length of the string. It can be described as a bulge appearing in the initial string, starting from the string of small, classically stable radius, expanding to a fat string of large, classically unstable (to expansion) radius and then returning back to the string of small radius along its length. This configuration is the bounce point of a corresponding O(2) symmetric instanton, which we can determine numerically. Once the bulge appears it explodes in real time. The kink soliton anti-soliton pair recede from each other along the length of the string with a velocity that quickly approaches the speed of light, leaving behind a fat tube. At the same time the radius of the fat tube that is being formed, expands (transversely) as it is no longer classically stable, converting false vacuum to the true vacuum with ever diluting magnetic field within. The rate of this expansion is determined by the energy difference between the true vacuum and the false vacuum. Our analysis could be applied to a network, of cosmic strings formed in the very early universe or vortex lines in a superheated superconductor., Comment: 13 pages, 4 figures

We consider the decay of vortices trapped in the false vacuum of a theory of scalar electrodynamics in 2+1 dimensions. The potential is inspired by models with intermediate symmetry breaking to a metastable vacuum that completely breaks a U(1) symmetry, while in the true vacuum the symmetry is unbroken. The false vacuum is unstable through the formation of true vacuum bubbles; however, the rate of decay can be extremely long. On the other hand, the false vacuum can contain metastable vortex solutions. These vortices contain the true vacuum inside in addition to a unit of magnetic flux and the appropriate topologically nontrivial false vacuum outside. We numerically establish the existence of vortex solutions which are classically stable; however, they can decay via tunneling. In general terms, they tunnel to a configuration which is a large, thin-walled vortex configuration that is now classically unstable to the expansion of its radius. We compute an estimate for the tunneling amplitude in the semi-classical approximation. We believe our analysis would be relevant to superconducting thin films or superfluids., Comment: 27 pages, 9 figures

We study the behavior of a quantum gyroscope, that is, a quantum system which singles out a direction in space in order to measure certain properties of incoming particles such as the orientation of their spins. We show that repeated Heisenberg interactions of the gyroscope with several incoming spin-1/2 particles provides a simple model of decoherence which exhibits both relaxation and dephasing. Focusing on the semiclassical limit, we derive equations of motion for the evolution of a coherent state and investigate the evolution of a superposition of such states. While a coherent state evolves on a timescale given by the classical ratio of the angular momentum of the gyroscope to that of the incoming particles, dephasing acts on a much shorter timescale that depends only on the angular difference of the states in the superposition., Comment: 7 pages, 5 figures

To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For models in which a two-state system interacts with a dynamical environment, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics., Comment: 4 pages, 2 figures

In this article, inspired by Lawrence Krauss' plenary talk at the 2007 CAP congress, the relation between faith and science is examined., Comment: 9 pages. To be published in Physics In Canada

We investigate, via Monte Carlo simulations, the phase structure of a system of closed, nonintersecting but otherwise non-interacting, loops in 3 Euclidean dimensions. The loops correspond to closed trajectories of massive particles and we find a phase transition as a function of their mass. We identify the order parameter as the average length of the loops at equilibrium. This order parameter exhibits a sharp increase as the mass is decreased through a critical value, the behaviour seems to be a cross-over transition. We believe that the model represents an effective description of the broken-symmetry sector of the 2+1 dimensional abelian Higgs model, in the extreme strong coupling limit. The massive gauge bosons and the neutral scalars are decoupled, and the relevant low-lying excitations correspond to vortices and anti-vortices. The functional integral can be approximated by a sum over simple, closed vortex loop configurations. We present a novel fashion to generate non-intersecting closed loops, starting from a tetrahedral tessellation of three space. The two phases that we find admit the following interpretation: the usual Higgs phase and a novel phase which is heralded by the appearance of effectively infinitely long loops. We compute the expectation value of the Wilson loop operator and that of the Polyakov loop operator. The Wilson loop exhibits perimeter law behaviour in both phases implying that the transition corresponds neither to the restoration of symmetry nor to confinement. The effective interaction between external charges is screened in both phases, however there is a dramatic increase in the polarization cloud in the novel phase as shown by the energy shift introduced by the Wilson loop., Comment: 10 pages, 20 figures, color viewing helpful; greatly expanded, published version; title changed

These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum mechanics. No prior exposure to path integrals is assumed, however. The path integral is a formulation of quantum mechanics equivalent to the standard formulations, offering a new way of looking at the subject which is, arguably, more intuitive than the usual approaches. Applications of path integrals are as vast as those of quantum mechanics itself, including the quantum mechanics of a single particle, statistical mechanics, condensed matter physics and quantum field theory. After an introduction including a very brief historical overview of the subject, we derive a path integral expression for the propagator in quantum mechanics, including the free particle and harmonic oscillator as examples. We then discuss a variety of applications, including path integrals in multiply-connected spaces, Euclidean path integrals and statistical mechanics, perturbation theory in quantum mechanics and in quantum field theory, and instantons via path integrals. For the most part, the emphasis is on explicit calculations in the familiar setting of quantum mechanics, with some discussion (often brief and schematic) of how these ideas can be applied to more complicated situations such as field theory., Comment: 55 pages, 23 figures. Lectures given at Rencontres du Vietnam: VIth Vietnam School of Physics, Vung Tau, Vietnam, 27 December 1999 - 8 January 2000

We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument., Comment: 11 pages, UdeM-LPN-TH-130