Tests of time-reversal invariance in complex systems

The random-matrix theory for the effects of time-reversal non-invariance (TRNI) on energy level, strength and cross-section fluctuations in complex systems is reviewed. Applied to the compound-nuclear data this gives bounds on rms TRNI matrix elements. Using a fluctuation-free form of statistical spectroscopy bounds on α, the relative magnitude of the TRNI nucleon-nucleon interaction, is deduced. In all three cases we find α ≲ (2–3) × 10⁻³ at high (∼ 99%) statistical confidence. Suggestions are made about experiments which should improve the bounds.     

Exceptional points in a microwave billiard with time-reversal invariance violation

We report on the experimental study of an exceptional point (EP) in a dissipative microwave billiard with induced time-reversal invariance (T) violation. The associated two-state Hamiltonian is non-Hermitian and nonsymmetric. It is determined experimentally on a narrow grid in a parameter plane around the EP. At the EP the size of T violation is given by the relative phase of the eigenvector components. The eigenvectors are adiabatically transported around the EP, whereupon they gather geometric phases and in addition geometric amplitudes different from unity.     

The Fermi to Gamow-Teller mixing ratio of theβ + decay of52Mn and time-reversal invariance

To date, ten experimental measurements of the asymmetry parameter have been made for the positron decay of⁵²Mn. The Fermi to Gamow-Teller mixing ratioy can be deduced from such measurements and this quantity is important because the time-reversal violating amplitude is proportional toy/(1+y²). Our theoretical calculation using the Collective Model yieldsy=? 3.5×10^?4 for the deformation parameterβ=0.1 andy=? 4.6×10^?4 forβ=0.2. Such small values ofy are consistent with time-reversal invarisance.     

An angular correlation test of time-reversal invariance

A test of time-reversal invariance in electromagnetic transitions is proposed in which all possible two-gamma angular correlations in a triple cascade are measured. The results can be combined to yield a term proportional to cos η.     

Adiabatic invariants induced by perturbation to form invariance of mechanico-electrical systems

This Letter focuses on perturbation to form invariance of mechanico-electrical systems. Criteria and structural equations for form invariance after disturbance are proposed. Considering perturbation of all the infinitesimal generators, a new type of adiabatic invariant induced by perturbation to form invariance of the system is reported.     

An experimental study on time-reversal invariance in nuclear gamma decay

Time-reversal invariance was studied by measuring γ-γ coincidences in ³⁶Cl after the capture of polarized thermal neutrons. The contribution of the time non-invariant amplitude for γ-decay to the total amplitude was determined to be (0.8±2.3) · 10⁻³, thus indicating no violation of T-invariance.     

Topological invariance in supersymmetric theories with a continuous spectrum

We calculate the superpartition function tr(?1)^F_e?βH with a continuous spectrum. This object depends explicitly on β although it is a topological invariant with respect to compact perturbations of the potential. We show that it can be evaluated by reducing the relevant functional integral to an integral over constant configurations. The relationship with the open-space trace theorem of Callias, Bott and Seeley is discussed.     

Discover potential in a search for time-reversal invariance violation in nuclei

Time reversal invariance violating (TRIV) effects in low energy physics could be very important in searching for new physics, being complementary to neutron and atomic electric dipole moment (EDM) measurements. In this relation, we discuss a sensitivity of some TRIV observables to different models of time-reversal (CP) violation and their dependencies on nuclear structure. As a measure of a sensitivity of TRIV effects to the value of TRIV nucleon coupling constant, we introduce a coefficient of a “discovery potential”, which shows a possible factor for improving the current limits of the EDM experiments by measuring nuclear TRIV effects.     

General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.     

Topological invariants for fractional quantum hall states

We calculate a topological invariant, whose value would coincide with the Chern number in the case of integer quantum Hall effect, for fractional quantum Hall states. In the case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In the case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot uniquely label distinct states.     

Fermi systems with strong forward scattering

We review the theory of interacting Fermi systems whose low-energy physics is dominated by forward scattering, that is scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids as well as several important non-Fermi-liquid phases: one-dimensional Luttinger liquids, systems with long-range interactions, and fermions coupled to a gauge field. We report results for the critical dimensions separating different 'universality classes' and discuss the behaviour of physical quantities such as the momentum distribution function, the single-particle propagator and low-energy response functions in each class. The renormalization group for Fermi systems will be reviewed and applied as a link between microscopic models and effective lowenergy theories. Particular attention is paid to conservation laws, which constrain any effective low-energy theory of interacting Fermi systems. In scattering processes with small momentum transfers the velocity of each scattering particle is (almost) conserved. This asymptotic conservation law leads to non-trivial cancellations of Feynman diagrams and other simplifications, making thus possible a non-perturbative treatment of forward scattering via Ward identities or bosonization techniques.     

Topological invariants for anomalous Floquet higher-order topological insulators

We review the recent development in constructing higher-order topological band insulators under strong periodic drivings. In particular, we focus on various approaches in formulating the anomalous Floquet topological invariants beyond (quasi-)static band topology, and compare their different physical consequences.