Time Reversal Transformation Research Articles

Model-independent search for T violation with T2HK and DUNE

We consider the time reversal (T) transformation in neutrino oscillations in a model-independent way by comparing the observed transition probabilities at two different baselines at the same neutrino energy. We show that, under modest model assumptions, if the transition probability Pνμ→νe around Eν ≃ 0.86 GeV measured at DUNE is smaller than the one at T2HK the T symmetry has to be violated. Experimental requirements needed to achieve good sensitivity to this test for T violation are to obtain enough statistics at DUNE for Eν ≲ 1 GeV (around the 2nd oscillation maximum), good energy resolution (better than 10%), and near-detector measurements with a precision of order 1% or better.

Integrable coupled bosonic massive Thirring model and its nonlocal reductions

A coupled bosonic massive Thirring model (BMTM), involving an interaction between the two independent spinors, is introduced and shown to be integrable. By incorporating suitable reductions between the field components of the coupled BMTM, five novel integrable models with various type of nonlocal interactions are constructed. Lax pairs satisfying the zero curvature condition are obtained for the coupled BMTM and for each of the related nonlocal models. An infinite number of conserved quantities are derived for each of these models which confirms the integrability of the systems. It is shown that the coupled BMTM respects important symmetries of the original BMTM such as parity, time reversal, global U(1)-gauge and the proper Lorentz transformations. Similarly, all the nonlocal models obtained from the coupled BMTM remain invariant under combined operation of parity and time reversal transformations. However, it is found that only one of the nonlocal models is invariant under proper Lorentz transformation and two other models are invariant under global U(1)-gauge transformation. By using ultralocal Poisson bracket relations among the elements of the Lax operator, it is shown that the coupled BMTM and one of the nonlocal models are completely integrable in the Liouville sense.

Dynamical Asymmetries, the Bayes’ Theorem, Entanglement, and Intentionality in the Brain Functional Activity

We discuss the asymmetries of dynamical origin that are relevant to functional brain activity. The brain is permanently open to its environment, and its dissipative dynamics is characterized indeed by the asymmetries under time translation transformations and time-reversal transformations, which manifest themselves in the irreversible “arrow of time”. Another asymmetry of dynamical origin arises from the breakdown of the rotational symmetry of molecular electric dipoles, triggered by incoming stimuli, which manifests in long-range dipole-dipole correlations favoring neuronal correlations. In the dissipative model, neurons, glial cells, and other biological components are classical structures. The dipole vibrational fields are quantum variables. We review the quantum field theory model of the brain proposed by Ricciardi and Umezawa and its subsequent extension to dissipative dynamics. We then show that Bayes’ theorem in probability theory is intrinsic to the structure of the brain states and discuss its strict relation with entanglement phenomena and free energy minimization. The brain estimates the action with a higher Bayes probability to be taken to produce the aimed effect. Bayes’ rule provides the formal basis of the intentionality in brain activity, which we also discuss in relation to mind and consciousness.

Symmetry resolved entanglement of excited states in quantum field theory. Part III. Bosonic and fermionic negativity

In two recent works, we studied the symmetry resolved Rényi entropies of quasi-particle excited states in quantum field theory. We found that the entropies display many model-independent features which we discussed and analytically characterised. In this paper we extend this line of investigation by providing analytical and numerical evidence that a similar universal behavior arises for the symmetry resolved negativity. In particular, we compute the ratio of charged moments of the partially transposed reduced density matrix as an expectation value of twist operators. These are “fused” versions of the more traditionally used branch point twist fields and were introduced in a previous work. The use of twist operators allows us to perform the computation in an arbitrary number of spacial dimensions. We show that, in the large-volume limit, only the commutation relations between the twist operators and local fields matter, and computations reduce to a purely combinatorial problem. We address some specific issues regarding fermionic excitations, whose treatment requires the notion of partial time-reversal transformation, and we discuss the differences and analogies with their bosonic counterpart. We find that although the operation of partial transposition requires a redefinition for fermionic theories, the ratio of the negativity moments between an excited state and the ground state is universal and identical for fermions and bosons as well as for a large variety of very different states, ranging from simple qubit states to the excited states of free quantum field theories. Our predictions are tested numerically on a 1D Fermi chain.

Noninvertible Time-Reversal Symmetry.

In gauge theory, it is commonly stated that time-reversal symmetry only exists at θ=0 or π for a 2π-periodic θ angle. In this Letter, we point out that in both the free Maxwell theory and massive QED, there is a noninvertible time-reversal symmetry at every rational θ angle, i.e., θ=πp/N. The noninvertible time-reversal symmetry is implemented by a conserved, antilinear operator without an inverse. It is a composition of the naive time-reversal transformation and a fractional quantum Hall state. We also find similar noninvertible time-reversal symmetries in non-Abelian gauge theories, including the N=4 SU(2) super Yang-Mills theory along the locus |τ|=1 on the conformal manifold.

A framework for nonrelativistic isotropic models based on generalized uncertainty principles

The existence of a fundamental length scale in nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg uncertainty principle may be expected. Despite the attention given to this possibility in the past decades, there has been no common framework for a systematic investigation of so-called generalized uncertainty principles (GUP). In this work we provide such a framework in the context of nonrelativistic quantum mechanics. Our approach is based on very few assumptions: there is a fundamental length scale, space isotropy, invariance under parity and time reversal transformations, and symmetricity of the position and momentum operators. We show that simple dimensional analysis allows building a common framework for isotropic models based on GUP (we call those iGUP models). We discuss some popular GUP models in this context after elaborating on relevant theoretical aspects of the framework. At last, we translate current bounds on three often investigated GUP models into bounds on parameters of such common iGUP framework.

Fractional topological charge in lattice Abelian gauge theory

AbstractWe construct a non-trivial $U(1)/\mathbb {Z}_q$ principal bundle on T4 from the compact U(1) lattice gauge field by generalizing Lüscher’s constriction so that the cocycle condition contains $\mathbb {Z}_q$ elements (the ’t Hooft flux). The construction requires an admissibility condition on lattice gauge field configurations. From the transition function so constructed, we have the fractional topological charge that is $\mathbb {Z}_q$ one-form gauge invariant and odd under the lattice time reversal transformation. Assuming a rescaling of the vacuum angle θ → qθ suggested from the Witten effect, our construction provides a lattice implementation of the mixed ’t Hooft anomaly between the $\mathbb {Z}_q$ one-form symmetry and the time reversal symmetry in the U(1) gauge theory with matter fields of charge $q\in 2\mathbb {Z}$ when θ = π, which was studied by Honda and Tanizaki [J. High Energy Phys. 12, 154 (2020)] in the continuum framework.

Antiferromagnetic Chern insulator in centrosymmetric systems

An antiferromagnetic Chern insulator (AFCI) can exist if the effect of the time-reversal transformation on the electronic state cannot be compensated by a space group operation. The AFCI state with collinear magnetic order is already realized in noncentrosymmetric honeycomb structures through the Kane-Mele-Hubbard model. In this paper, we demonstrate the existence of the collinear AFCI in a square lattice model which preserves the inversion symmetry. Our study relies on the time-reversal-invariant Harper-Hofstadter-Hubbard model extended by a next-nearest-neighbor hopping term including spin-orbit coupling and a checkerboard potential. We show that an easy $z$-axis AFCI appears between the band insulator at weak and the easy $xy$-plane AF Mott insulator at strong Hubbard repulsion provided the checkerboard potential is large enough. The close similarity between our results and the results obtained for the noncentrosymmetric Kane-Mele-Hubbard model suggests the AFCI as a generic consequence of spin-orbit coupling and strong electronic correlation which exists beyond a specific model or lattice structure. An AFCI with the electronic and the magnetic properties originating from the same strongly interacting electrons is promising candidate for a strong magnetic blue shift of the charge gap below the N\'eel temperature and for realizing the quantum anomalous Hall effect at higher temperatures so that applications for data processing become possible.

Parton distributions: Functional complexity and Lorentz parametrization

In this paper, we focus on the study of the functional complexity of the Lorentz parametrizing functions in connection with the time-reversal transformations. We argue that the interactions encoded in the corresponding correlators of nonlocal quark(–gluon) operators generate additional sources of functional complexity for the parametrizing functions which are not discussed in the literature. We also revisit the Lorentz parametrization of different correlators given by the hadron matrix elements of the nonlocal operators. The evidences for the new parametrizing function existence have been presented.

Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian

The effect of monochromatic circularly or linearly polarized laser on the Hofstadter butterfly in the square lattice is studied theoretically using Floquet theory. In the absence of laser, the butterfly has a self-similar, fractal structure against the magnetic flux ϕ with particle–hole symmetry and reflection symmetry about ϕ = 1/2. The observed two symmetric features are preserved by the sub-lattice symmetry and the symmetry property of the model with respect to time-reversal, respectively. As the system is exposed to a circularly polarized light, the Hofsatdter butterfly in equilibrium is deformed by degrading the above two symmetries to the inversion symmetry about energy E = 0 and ϕ = 1/2. Our study show that, the deformation of Hofstatder butterfly is due to the breaking of both the sub-lattice symmetry and the time-reversal transformation related symmetry of the system by the circularly polarized light. The inversion symmetry is preserved because the Hamiltonian at ϕ and 1 − ϕ is connected through the sub-lattice transformation. Focusing on the small flux region, we study the influence of circularly polarized light on the Landau level. A quantitative description on the Landau level is given by considering the effective Hamiltonian at high frequency. On the other hand, the linearly polarized light deforms the original Hofstadter butterfly by breaking the rotational symmetry while preserving sub-lattice and the time-reversal transformation related symmetry. Further, we study the influence of the periodic drive on the Chern number of the lowest band in the middle Floquet copy within the off-resonance regime. We find that strong circularly polarized light will change the Chern number. For linearly polarized light, the Chern number will not change and the values stay independent of laser polarization direction. Our work highlights the generic features expected for the periodically driven Hofstadter problem on square lattice and provide the strategy of engineering the Hofstadter butterfly with laser.

Multi-Band Parity-Time-Symmetric Wireless Power Transfer Systems for ISM-Band Bio-Implantable Applications

Modern wireless implantable medical devices face escalating demand for lightweight and low-cost wireless solutions exploited to wake up sensors and transfer data. In this paper, we propose and experimentally demonstrate the efficient, multi-band wireless power transfer (WPT) systems that are symmetric with respect to the combined parity ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> ) and time reversal ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ) transformations (i.e., space-time reflection symmetry). In analogy with non-Hermitian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PT</i> -symmetric physical systems that can have branching real eigenfrequencies as a function of the dimensionless non-Hermiticity and the coupling factor, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PT</i> -symmetric WPT system exhibits multi-band and/or wideband operations via adjustment of the non-Hermiticity (i.e., quality-factor of resonant tanks) and their mutual inductive or capacitive coupling strength. Here, we put forward design and implementation for achieving dual-band, tri-band, and wideband <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PT</i> -symmetric WPT systems, capable of operating in the industrial, scientific, and medical (ISM) bands (27.12 MHz and 40.68 MHz) with high transmission efficiency. This compact and low-cost WPT technique may be exploited in many practical applications, such as wireless charging of bioimplants and wearables, as well as interrogation of battery-free medical devices and internet-of-things (IoT) sensors to assist smart healthcare.

Time-reversal symmetry breaking and emergence in driven-dissipative Ising models

Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS), two pillars of statistical mechanics, are both broken in generic driven-dissipative systems. These systems rather lead to non-equilibrium steady states far from thermal equilibrium. Driven-dissipative Ising-type models, however, are widely believed to exhibit effective thermal critical behavior near their phase transitions. Contrary to this picture, we show that both the FDR and TRS are broken even macroscopically at, or near, criticality. This is shown by inspecting different observables, both even and odd operators under time-reversal transformation, that overlap with the order parameter. Remarkably, however, a modified form of the FDR as well as TRS still holds, but with drastic consequences for the correlation and response functions as well as the Onsager reciprocity relations. Finally, we find that, at criticality, TRS remains broken even in the weakly-dissipative limit.

Measuring the Topological Time Irreversibility of Time Series With the Degree-Vector-Based Visibility Graph Method

Time irreversibility of a time series, which can be defined as the variance of properties under the time-reversal transformation, is a cardinal property of non-equilibrium systems and is associated with predictability in the study of financial time series. Recent pieces of literature have proposed the visibility-graph-based approaches that specifically refer to topological properties of the network mapped from a time series, with which one can quantify different degrees of time irreversibility within the sets of statistically time-asymmetric series. However, all these studies have inadequacies in capturing the time irreversibility of some important classes of time series. Here, we extend the visibility-graph-based method by introducing a degree vector associated with network nodes to represent the characteristic patterns of the index motion. The newly proposed method is parameter-free and temporally local. The validation to canonical synthetic time series, in the aspect of time (ir)reversibility, illustrates that our method can differentiate a non-Markovian additive random walk from an unbiased Markovian walk, as well as a GARCH time series from an unbiased multiplicative random walk. We further apply the method to the real-world financial time series and find that the price motions occasionally equip much higher time irreversibility than the calibrated GARCH model does.

Testing CPT symmetry in ortho-positronium decays with positronium annihilation tomography

Charged lepton system symmetry under combined charge, parity, and time-reversal transformation (CPT) remains scarcely tested. Despite stringent quantum-electrodynamic limits, discrepancies in predictions for the electron–positron bound state (positronium atom) motivate further investigation, including fundamental symmetry tests. While CPT noninvariance effects could be manifested in non-vanishing angular correlations between final-state photons and spin of annihilating positronium, measurements were previously limited by knowledge of the latter. Here, we demonstrate tomographic reconstruction techniques applied to three-photon annihilations of ortho-positronium atoms to estimate their spin polarisation without magnetic field or polarised positronium source. We use a plastic-scintillator-based positron-emission-tomography scanner to record ortho-positronium (o-Ps) annihilations with single-event estimation of o-Ps spin and determine the complete spectrum of an angular correlation operator sensitive to CPT-violating effects. We find no violation at the precision level of 10−4, with an over threefold improvement on the previous measurement.

Chiral states and nonreciprocal phases in a Josephson junction ring

In this work, we propose how to load and manipulate chiral states in a Josephson junction ring in the so called transmon regimen. We characterise these states by their symmetry properties under time reversal and parity transformations. We describe an explicit protocol to load and detect the states within a realistic set of circuit parameters and show simulations that reveal the chiral nature. Finally, we explore the utility of these states in quantum technological nonreciprocal devices.

Symmetry decomposition of negativity of massless free fermions

We consider the problem of symmetry decomposition of the entanglement negativity in free fermionic systems. Rather than performing the standard partial transpose, we use the partial time-reversal transformation which naturally encodes the fermionic statistics. The negativity admits a resolution in terms of the charge imbalance between the two subsystems. We introduce a normalised version of the imbalance resolved negativity which has the advantage to be an entanglement proxy for each symmetry sector, but may diverge in the limit of pure states for some sectors. Our main focus is then the resolution of the negativity for a free Dirac field at finite temperature and size. We consider both bipartite and tripartite geometries and exploit conformal field theory to derive universal results for the charge imbalance resolved negativity. To this end, we use a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in the Riemann surface defining the entanglement. We interestingly find that the entanglement negativity is always equally distributed among the different imbalance sectors at leading order. Our analytical findings are tested against exact numerical calculations for free fermions on a lattice.

Dynamical instantons and activated processes in mean-field glass models

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical p-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

{mathcal{P}}{mathcal{T}}-Symmetric Effective Model for Nonequilibrium Phase Transitions in a Dissipative Fermionic Mott Insulator Chain

Nonequilibrium phase transitions in open dissipative systems can be described as instabilities in the spectra and wavefunctions of effective non-Hermitian Hamiltonians invariant under simultaneous parity (boldsymbol{mathcal{P}}) and time-reversal (boldsymbol{mathcal{T}}) transformations. The degree of non-Hermiticity reflects the strength of the external drive and dissipation, and the transition is described as a loss of the boldsymbol{mathcal{P}}boldsymbol{mathcal{T}} symmetry of the solutions corresponding to stationary low-drive dynamics. This approach has been successfully applied to spin, superconducting, and Mott insulator systems. However, the microscopic foundations for the employed phenomenological models are currently lacking. Here we propose a microscopic mechanism leading to the boldsymbol{mathcal{P}}boldsymbol{mathcal{T}}-symmetric effective model in the context of the nonequilibrium Mott transition in a dissipative Hubbard chain. Our model comprises a half-filled fermionic Hubbard chain subject to a constant electric field. The dissipation is introduced via the electron-phonon coupling. We obtain the explicit expressions for the non-Hermitian parameter in terms of the electron-phonon coupling strength and driving field. Analyzing the implications of microscopic model, we find a re-entrant Mott insulator with the increasing electric field for phonon density of states that increases slower than the square of the energy (such as in one or two dimensions), or varies non-monotonously with energy.

XFe4Ge2(X=Y,Lu) and Mn3Pt : Filling-enforced magnetic topological metals

Magnetism, coupled with nontrivial band topology, can bring about many interesting and exotic phenomena, so that magnetic topological materials have attracted persistent research interest. However, compared with non-magnetic topological materials (TMs), the magnetic TMs are less studied, since their magnetic structures and topological phase transitions are usually complex and the first-principles predictions are usually sensitive on the effect of Coulomb interaction. In this work, we present a comprehensive investigation of XFe4Ge2 (X = Y, Lu) and Mn3Pt, and find these materials to be filling-enforced magnetic topological metals. Our first-principles calculations show that XFe4Ge2 (X = Y, Lu) host Dirac points near the Fermi level at high symmetry point S. These Dirac points are protected by PT symmetry (P and T are inversion and time-reversal transformations, respectively) and a 2-fold screw rotation symmetry. Moreover, through breaking PT symmetry, the Dirac points would split into Weyl nodes. Mn3Pt is found to host 4-fold degenerate band crossings in the whole high symmetry path of A-Z. We also utilize the GGA+U scheme to take into account the effect of Coulomb repulsion and find that the filling-enforced topological properties are naturally insensitive on U.

Deconfinement to confinement as PT phase transition

We consider SU(N) QCD in a new quadratic gauge which highlights certain characteristic of the theory in the non-perturbative sector. By considering natural hermiticity property of the ghost fields we cast this model as non-Hermitian but symmetric under combined Parity (P) and Time reversal (T) transformations. We explicitly study the PT phase transition in this model. This is very first such study in the non-Hermitian gauge theory. The ghost fields condensate which give rise to spontaneous breaking of PT symmetry. This leads to realize the transition from deconfined phase to confined phase as a PT phase transition in this system. The hidden C-symmetry in this system is identified as inner automorphism in this theory. Explicit representation is constructed for the C-symmetry.