Time Reversal Operator Research Articles

Density functional perturbation theory for lattice dynamics with fully relativistic ultrasoft pseudopotentials: The magnetic case

We extend density functional perturbation theory for lattice dynamics with fully relativistic ultrasoft pseudopotentials to magnetic materials. Our approach is based on the application of the time-reversal operator to the Sternheimer linear system and to its self-consistent solutions. Moreover, we discuss how to include in the formalism the symmetry operations of the magnetic point group which require the time-reversal operator. We validate our implementation by comparison with the frozen phonon method in fcc Ni and in a monatomic ferromagnetic Pt wire.

Bragg-induced oscillations in non-PT complex photonic lattices

We investigate Bragg-induced oscillations in complex non-PT periodic structures, that is, a periodic medium with gain and loss and not necessarily symmetric under the combined action of parity and time reversal operations. We compare our analytic results based on the expansion of the optical field in Bragg-resonant plane waves with a direct numerical integration of the paraxial wave equation beyond the shallow potential approximation and using a wide Gaussian beam as initial condition. In particular, we study under which conditions a mode trapping phenomenon may still be observed and to inspect how the energy exchange between the spectral modes takes place during propagation in this more general class of asymmetric complex potentials.

Spatial anisotropy of the Kondo screening cloud in a type-II Weyl semimetal

We theoretically study the Kondo screening of a spin-1/2 magnetic impurity in the bulk of a type-II Weyl semimetal (WSM) by use of the variational wave function method. We consider a type-II WSM model with two Weyl nodes located on the $k_z$-axis, and the tilting of the Weyl cones are along the $k_x$ direction. Due to co-existing electron and hole pockets, the density of states at the Fermi energy becomes finite, leading to a significant enhancement of Kondo effect. Consequently, the magnetic impurity and the conduction electrons always form a bound state, this behavior is distinct from that in the type-I WSMs, where the bound state is only formed when the hybridization exceeds a critical value. Meanwhile, the spin-orbit coupling and unique geometry of the Fermi surface lead to strongly anisotropic Kondo screening cloud in coordinate space. The tilting terms break the rotational symmetry of the type-II WSM about the $k_z$-axis, but the system remains invariant under a combined transformation $\mathcal{T}R^{y}(\pi)$, where $\mathcal{T}$ is the time-reversal operation and $R^{y}(\pi)$ is the rotation about the $y$-axis by $\pi$. Largely modified diagonal and off-diagonal components of the spin-spin correlation function on three principal planes reflect this change in band symmetry. Most saliently, the tilting terms trigger the emergence of non-zero off-diagonal components of spin-spin correlation function on the $x$-$z$ principal plane.

The geometrical properties of parity and time reversal operators in two dimensional spaces

The parity operator P and time reversal operator T are two important operators in the quantum theory, in particular, in the PT-symmetric quantum theory. By using the concrete forms of P and T, we discuss their geometrical properties in two dimensional spaces. It is showed that if T is given, then all P links with the quadric surfaces; if P is given, then all T links with the quadric curves. Moreover, we give out the generalized unbroken PT-symmetric condition of an operator. The unbroken PT-symmetry of a Hermitian operator is also showed in this way.

Reconstruction of Photoacoustic Tomography Inside a Scattering Layer Using a Matrix Filtering Method

Photoacoustic (PA) tomography (PAT) has potential for use in brain imaging due to its rich optical contrast, high acoustic resolution in deep tissue, and good biosafety. However, the skull often poses challenges for transcranial brain imaging. The skull can cause severe distortion and attenuation of the phase and amplitude of PA waves, which leads to poor resolution, low contrast, and strong noise in the images. In this study, we propose an image reconstruction method to recover the PA image insider a skull-like scattering layer. This method reduces the scattering artifacts by combining a correlation matrix filter and a time reversal operator. Both numerical simulations and PA imaging experiments demonstrate that the proposed approach effectively improves the image quality with less speckle noise and better signal-to-noise ratio. The proposed method may improve the quality of PAT in a complex acoustic scattering environment, such as transcranial brain imaging.

Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server.

Two new programs, MTENSOR and TENSOR, hosted on the open-access website known as the Bilbao Crystallographic Server, are presented. The programs provide automatically the symmetry-adapted form of tensor properties for any magnetic or non-magnetic point group or space group. The tensor is chosen from a list of 144 known tensor properties gathered from the scientific literature or, alternatively, the user can also build a tensor that possesses an arbitrary intrinsic symmetry. Four different tensor types are considered: equilibrium, transport, optical and nonlinear optical susceptibility tensors. For magnetically ordered structures, special attention is devoted to a detailed discussion of the transformation rules of the tensors under the time-reversal operation 1'. It is emphasized that for non-equilibrium properties it is the Onsager theorem, and not the constitutive relationships, that indicates how these tensors transform under 1'. In this way it is not necessary to restrict the validity of Neumann's principle. New Jahn symbols describing the intrinsic symmetry of the tensors are introduced for several transport and optical properties. In the case of some nonlinear optical susceptibilities of practical interest, an intuitive method is proposed based on simple diagrams, which allows easy deduction of the action of 1' on the susceptibilities. This topic has not received sufficient attention in the literature and, in fact, it is usual to find published results where the symmetry restrictions for such tensors are incomplete.

Phase-conjugate mirror for water waves driven by the Faraday instability

The Faraday instability appears on liquid baths submitted to vertical oscillations above a critical value. The pattern of standing ripples at half the vibrating frequency that results from this parametric forcing is usually shaped by the boundary conditions imposed by the enclosing receptacle. Here, we show that the time modulation of the medium involved in the Faraday instability can act as a phase-conjugate mirror--a fact which is hidden in the extensively studied case of the boundary-driven regime. We first demonstrate the complete analogy with the equations governing its optical counterpart. We then use water baths combining shallow and deep areas of arbitrary shapes to spatially localize the Faraday instability. We give experimental evidence of the ability of the Faraday instability to generate counterpropagating phase-conjugated waves for any propagating signal wave. The canonical geometries of a point and plane source are implemented. We also verify that Faraday-based phase-conjugate mirrors hold the genuine property of being shape independent. These results show that a periodic modulation of the effective gravity can perform time-reversal operations on monochromatic propagating water waves, with a remarkable efficiency compared with wave manipulation in other fields of physics.

Imaging a crack in a thin plate by reverse time migration with dispersive flexural waves

A method is presented to image a crack in a thin plate by reverse time migration (RTM) with flexural waves. Two time reversal (TR) operations are involved in this method. First, the scattered flexural wave at a receiver is reversed in time and re-emitted from the receiver. It propagates backward in the host plate. The spread of the wavelet due to dispersion is compensated by the TR operation. Then, at a given target point, the wave is time reversed again. The time-reversed version of the backward wave is correlated to the forward wave that comes from the original source in the same host plate. As a result, an ellipsoidal image with foci of the source and receiver is obtained by calculating the cross-correlations of the forward field from the source and the backward field from the receiver. The image of the crack is then obtained by superimposing the ellipses acquired by different source–receiver pairs. The resolution of the image is improved using a modified imaging condition. The method is then validated by numerical simulations to image three types of cracks using the synthesized scattered waves.

A time-reversal imaging system for buried objects in layered media using complex images Green’s functions

In this paper, the three-dimensional problem of detection and localization of buried metallic objects inside a multilayered medium is studied. Decomposition of the time-reversal operator (DORT) is used as the inversion algorithm in the imaging method. In this approach, one has to analyze the time-reversal (TR) operator obtained by using the multistatic data matrix (MDM) of a TR array. To attain MDM in the forward problem, full-wave simulation results from a commercial simulation software are used. For synthetic retransmission of signals in this inverse problem, determination of the appropriate medium Green’s function is required. Here, for the first time the complex images technique is employed in calculating the required Green’s functions. The complex images technique gives a closed-form Green's function, instead of evaluating time-consuming numerical integrals resulting in a fast and accurate Green’s function calculation. Using singular value decomposition of the MDM at a frequency range of 1–3 GHz and synthesized DORT method, images are constructed. Numerical results show the accuracy of the proposed approach in the detection and localization of buried objects. Furthermore, noise effect and sensitivity analysis on layers’ permittivity values are studied. The results confirm the robustness of the method against noise and uncertain layers parameters.

Roads to the past: how to go and not to go backward in time in quantum theories

In this article I shall defend, against the conventional understanding of the matter, that two coherent and tenable approaches to time reversal can be suitably introduced in standard quantum mechanics: an “orthodox” approach that demands time reversal to be represented in terms of an anti-unitary and anti-linear time-reversal operator, and a “heterodox” approach that represents time reversal in terms of a unitary, linear time-reversal operator. The rationale shall be that the orthodox approach in quantum theories assumes a relationalist metaphysics of time, according to which time reversal is nothing but motion reversal. But, when one shifts gears and turn to a substantivalist metaphysics of time the heterodox approach to time reversal in quantum mechanics comes up in a more natural way.

On-chip dynamic time reversal of light in a coupled-cavity system

We theoretically and experimentally demonstrate dynamic, all-linear time-reversal of infrared light in planar optical circuits for the first time. We propose that the oscillatory motion of the light stored in cavities can be time-reversed by fast nonadiabatic tuning of the frequency of eigenmodes of a coupled cavity system and experimentally demonstrate it using a system consisting of distant high-Q-factor two-dimensional photonic crystal cavities between which effective direct couplings are formed via line-defect waveguides. We also analyze the loss and methods to reduce the loss, as well as a theory that expands our system to realize general time-reversal operation for any input light.

Complex charges, time reversal asymmetry, and interior-boundary conditions in quantum field theory

While fundamental physically realistic Hamiltonians should be invariant under time reversal, time asymmetric Hamiltonians can occur as mathematical possibilities or effective Hamiltonians. Here, we study conditions under which non-relativistic Hamiltonians involving particle creation and annihilation, as come up in quantum field theory (QFT), are time asymmetric. It turns out that the time reversal operator T can be more complicated than just complex conjugation, which leads to the question which criteria determine the correct action of time reversal. We use Bohmian trajectories for this purpose and show that time reversal symmetry can be broken when charges are permitted to be complex numbers, where ‘charge’ means the coupling constant in a QFT that governs the strength with which a fermion emits and absorbs bosons. We pay particular attention to the technique for defining Hamiltonians with particle creation based on interior-boundary conditions, and we find them to generically be time asymmetric. Specifically, we show that time asymmetry for complex charges occurs whenever not all charges have equal or opposite phase. We further show that, in this case, the corresponding ground states can have non-zero probability currents, and we determine the effective potential between fermions of complex charge.

Tunable superconducting effective gap in graphene-TMDC heterostructures

Growth of graphene on monolayer transition-metal dichalcogenides presents opening on band gap and giant spin-orbit coupling which paves the way to achieve a useful hybrid structure for electronics and spintronics applications. Increase of the atomic number of transition-metal results in a large SOC, where eventually a band inversion appears in graphene-WSe2. We consider superconductor induction by proximity effect to the graphene-TMDC hybrid structure. As a necessity of formalism, we introduce a proper time-reversal and particle-hole symmetry operators, under which the 8 × 8 Dirac-Bogoliubov-de Gennes low-energy effective Hamiltonian is invariant. Resulting superconducting electron-hole excitations shows that, the essential dynamical parameters λIA,B and λR have significant effect on superconducting excitations and, specifically, subgap energy. Dependence of the superconducting energy excitation on chemical potential is explored. The signature of spin triplet p-wave pairing symmetry in the system is found to increase the subgap superconducting energy, in comparing to s-wave symmetry.

Anyonic symmetry, drifting potentials and non-Hermitian delocalization

We consider wave dynamics for a Schrödinger equation with a non-Hermitian Hamiltonian satisfying the generalized (anyonic) parity-time symmetry , where and are the parity and time-reversal operators. For a stationary potential, the anyonic phase φ just rotates the energy spectrum of in a complex plane, however, for a drifting potential the energy spectrum is deformed and the scattering and localization properties of the potential show intriguing behaviors arising from the breakdown of the Galilean invariance when . In particular, in the unbroken phase the drift makes a scattering potential barrier reflectionless, whereas for a potential well the number of bound states decreases as the drift velocity increases because of a non-Hermitian delocalization transition.

High-resolution imaging algorithm based on temporal focal characteristic of time-reversed signal

Although the high-resolution materials can improve the resolution of the conventional time-reversal imaging (TRI) algorithms, they also limit the applications of TRI. In this paper, a new TRI algorithm with high-resolution is presented. Since the proposed algorithm utilizes multiple time reversal operation steps to improve resolution, it can realize high-resolution without invoking any high-resolution materials. The results show the resolution of the proposed algorithm is superior to that of the conventional TRI.

Ultrasensitive, Parity–Time-Symmetric Wireless Reactive and Resistive Sensors

We propose a new readout paradigm for enhancing the performance of wireless resistive and reactive sensors. Here, we consider a passive resistor–inductor–capacitor sensor that is inductively coupled to an active reader, with the equivalent circuit of the whole telemetry system obeying the space-time reflection symmetry or the parity–time (PT) symmetry. As inspired by PT-symmetric quantum systems, this circuit has a non-Hermitian effective Hamiltonian that commutes with the antilinear, combined ${\mathcal {PT}}$ operator, where ${\mathcal {P}}$ and ${\mathcal {T}}$ are parity-inversion and time-reversal operators. We demonstrate that the PT-symmetric wireless sensor system, when compared to conventional interrogation techniques using a passive coil antenna, may provide significantly improved quality factor ( ${Q}$ -factor), sensing resolution, and sensitivity in response to the sensor’s reactance or resistance variation. Our results may have an impact on various wireless sensing, detection, and imaging systems, particularly for emerging micromachined sensors, miniature implants, wearables, and Internet-of-Things applications.

Feasibility Study of Steel Bar Corrosion Monitoring Using a Piezoceramic Transducer Enabled Time Reversal Method

Steel bars, which are commonly used as reinforcements in concrete structures, are slender rods and are good conduits for stress wave propagation. In this paper, a lead zirconate titanate (PZT)-based steel bar corrosion monitoring approach was proposed. Two PZT transducers are surface-bonded on the two ends of a steel rod, respectively. One works as actuator to generate stress waves, and the other functions as a sensor to detect the propagated stress waves. Time reverse technology was applied in this research to monitor the corrosion of the steel bars with a high signal to noise ratio (SNR). Accelerated corrosion experiments of steel bars were conducted. The anti-corrosion performance of the protected piezoceramic transducers was tested first, and then they were used to monitor the corrosion of the steel bar using the time reversal method. The degree of corrosion in the steel bar was determined by the ratio of mass loss during the experiment. The experimental results show that the peak values of the signal that were obtained by time reversal operation are linearly related to the degree of corrosion of the steel bar, which demonstrates the feasibility of the proposed approach for monitoring the corrosion of steel bars using the time reversal method enabled by piezoceramic transducers.

On evidence for negative energies and masses in the Dirac equation through a unitary time-reversal operator

We review the standards of relativistic quantum mechanics such as the Dirac equation under the concept of negative masses. We show that negative energies are acceptable provided the masses are simultaneously negative. Negative energy and mass anti-fermions are obtained from positive energy and mass fermions through a unitary PT transformation.

Through the Wall Imaging Using Ultrawideband Frequency Domain Sampling Method

In this paper, a novel ultrawideband (UWB) time reversal technique for through-the-wall imaging (TWI) is introduced. The proposed algorithm is based on utilization of spatial and UWB frequency data acquired by antenna array. Scattering data are obtained by transmitting a short pulse from the central transmitter and recording the received signal at each array element. Individual multistatic scattering data matrix according to each antenna is formed by casting the fine and coarse frequency samples of the scattering information. The resulting matrix is calibrated based on transmitter signal and fed into the DORT (French acronym for decomposition of the time reversal operator) algorithm. The performance of the proposed method is investigated numerically by applying it to discrete scatterers embedded in homogeneous and continuously random medium. Numerical results are presented to show the effectiveness and high efficiency of the proposed algorithm for TWI.

Imaging acoustic sources through scattering media by using a correlation full-matrix filter

In the inhomogeneous medium, acoustic scattering is always a fundamental challenge for photoacoustic imaging. We implement a correlation full-matrix filter (CFMF) combing with a time reversal operator to improve the imaging quality of acoustic sources in complex media. The correlation full-matrix filtering process extracts the direct wave component from the detected signal and preserve all the useful information at the same time. A location factor is considered in the time reversal operator to compensate for the image distortion and false contrast caused by the limited-view detection. The numerical simulations demonstrate that the proposed approach can perform good imaging quality with the higher image signal-noise ratio and better resolution in an acoustic scattering environment. This scheme might be applied to improve the photoacoustic imaging for inhomogeneous biological tissues.