Narrow Results

We show that the large, direct CP-violation parameter A_ππ=-C_ππ, reported by the BELLE collaboration in the decays , implies an unusual situation in which the presence of a very large difference between two strong-interaction phases (~ -110°) plays an essential role. We make the demonstration within a model of strong, two-body quasi-elastic interactions between physical hadrons. The model can accommodate a large difference between two strong-interaction phases, for which it provides a natural enhancement.

Shapere and Wilczek recently found some singular Lagrangian systems which spontaneously breaks time translation symmetry. The common feature of their models is that the energy functions are multi-valued in terms of the canonical phase space variables and the symmetry breaking ground states are all located at the brunching point singularities. By enlarging the phase space and making use of Dirac's theory on constrained Hamiltonian systems, we present the Hamiltonian description of some of the models discussed by Shapere and Wilczek and found that both the multi-valuedness and the brunching point singularities can be avoided, while the spontaneous breaking of time translation becomes more transparent. It is also shown that the breaking of time translation is always accompanied by the breaking of time reversal.

Since the CPT theorem was introduced in the 20th century, it has been one of the most important ongoing projects in particle physics. The CPT invariance helps to indicate if there are discrete symmetries in relativistic quantum mechanics (RQM), the answer to this question is ambiguous. This paper will mainly explain the answers via the timeline and point out misnomers and some missing concepts. We claim the answer to Are There Discrete Symmetries in Relativistic Quantum Mechanics is “yes, but no, no and yes again”. The most recent experiment shows the violation of CPT invariance is only $2\times {10}^{-10}$.

In this paper, we study the origin of the quantum particle entanglement. Particles will have one mixed wave function as soon as they are created, which are called quantum particle entanglement. Electron spin states are used as an example to discuss this topic. When two electrons are created simultaneously, they have two different mixed quantum spin states. Before the measurement of its spin, we cannot determine its spin state. However, as soon as the spin of one of the electrons is determined (measured), the spin of the other will definitely be in the opposite state, regardless of how far they are away from each other. This paper uses the mechanism that the wave packet spreads as soon as they are created and then the wave packet shrinks when it undergoes a measurement to interpret this spooky phenomenon mentioned above.

The parity and time reversal invariant actions, equations and their conjugated metric solutions are obtained in the context of a general relativistic model modified in order to suitably take into account discrete symmetries. The equations are not covariant however the predictions of the model, in particular its Schwarzschild metric solution in vacuum, only start to differ from those of General Relativity at the Post-Post-Newtonian order. No coordinate singularity (black hole) arises in the privileged coordinate system where the energy of gravity is found to vanish. Vacuum energies have no gravitational effects. A flat universe accelerated expansion phase is obtained without resorting to inflation nor a cosmological constant. The context may be promising to help us elucidate several outstanding enigmas such as the Pioneer anomalous blue-shift, flat galactic rotation curves or the universe voids.

We propose some methods for studying hadronic sequential two-body decays involving more spinning particles. It relies on the analysis of T-odd and T-even asymmetries, which are related to interference terms. The latter asymmetries turn out to be as useful as the former ones in inferring time reversal violating observables; these in turn may be sensitive, under some particular conditions, to possible contributions beyond the standard model. Our main result is that one can extract such observables even after integrating the differential decay width over almost all of the available angles. Moreover we find that the correlations based exclusively on momenta are quite general, since they provide as much information as those involving one or more spins. We generalize some methods already proposed in the literature for particular decay channels, but we also pick out a new kind of time reversal violating observables. Our analysis could be applied, for example, to data of LHCb experiment.

We construct a D₄ flavor model based on SU(3)_C ⊗SU(3)_L ⊗U(1)_X gauge symmetry responsible for fermion masses and mixings. The neutrinos get small masses from antisextets which are in a singlet and a doublet under D₄. If the D₄ symmetry is violated as perturbation by a Higgs triplet under SU(3)_L and lying in of D₄, the corresponding neutrino mass mixing matrix gets the most general form. In this case, the model can fit the experimental data in 2012 on neutrino masses and mixing. Our results show that the neutrino masses are naturally small and a little deviation from the tribimaximal neutrino mixing form can be realized. The quark masses and mixing matrix are also discussed. In the model under consideration, the CKM matrix can be different from the unit matrix. The scalar potential of the model is more simpler than those of the model based on S₃ and S₄. Assignation of VEVs to antisextets leads to the mixing of the new gauge bosons and those in the Standard Model. The mixing in the charged gauge bosons as well as the neutral gauge boson is considered.

The action for a massless particle in 4D Minkowski space–time has a worldline-time reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the ${𝒩}$-extended superparticle is shown to be anomalous when ${𝒩}$ is odd; in the supertwistor formalism this is because a CPT-violating worldline-Chern–Simons term is needed to preserve the chiral $U(1)$ gauge invariance. This accords with the fact that no massless ${𝒩}=1$ super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when ${𝒩}$ is even, but it has $2^{{𝒩}+1}$ states when $\frac{1}{2}{𝒩}$ is odd (e.g. the ${𝒩}=2$ hypermultiplet) in contrast to just $2^{{𝒩}}$ when $\frac{1}{2}{𝒩}$ is even (e.g. the ${𝒩}=4$ Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when $\frac{1}{2}{𝒩}$ is odd.

We investigate an alternative CPT-odd Lorentz-breaking QED which includes the Carroll–Field–Jackiw (CFJ) term of the Standard Model Extension (SME), writing the gauge sector in the action in a Palatini-like form, in which the vectorial field and the field-strength tensor are treated as independent entities. Interestingly, this naturally induces a Lorentz-violating mass term in the classical action. We study physical consistency aspects of the model both at classical and quantum levels.

Time-reversal had always been assumed to be a symmetry of physics at the fundamental level. In this paper we will explore the violations of time-reversal symmetry at the fundamental level and the consequence on thermodynamic systems. First, we will argue from current physics that the universe dynamics is not time-reversal invariant. Second, we will argue that any thermodynamic system cannot be isolated completely from the universe. We then discuss how these two make the dynamics of thermodynamics systems very weakly irreversible at the classical and quantum level. Since time-reversal is no longer a symmetry of realistic systems, the problem of how macroscopic irreversibility arises from microscopic reversibility becomes irrelevant because there is no longer microscopic reversibility. At the classical level of a thermodynamic system, we show that the H theorem of Boltzmann is still valid even without microscopic reversibility. We do this by deriving a modified H theorem, which still shows entropy monotonically increasing. At the quantum level, we explicitly show the effect of CP violation, small irreversible changes on the internal states of the nuclear and atomic energy levels of thermodynamic systems. Thus, we remove Loschmidt's objection to Boltzmann's ideas.

Is it possible, in principle, to measure the sign of the Lapse? We show that fermion dynamics distinguishes spacetimes having the same metric but different tetrads, for instance a Lapse with opposite sign. This sign might be a physical quantity not captured by the metric. We discuss its possible role in quantum gravity.

The epitome of a causal or anti-chronological behavior would be to see a clock running backwards in time. In this essay, we point out that this is indeed possible, but there is no problem with causality. What you see is not what is really happening. Locally, causality is always respected. However, our observation should be cause for pause to astronomers and cosmologists, who strictly observe events occurring at very large distances or very long ago and certainly not locally. It can be that what you see is not what you necessarily get.

Noise reduction and signal separation are important functions of acoustic signal processing. This study presents a detailed analysis for designing an acoustic signal processing procedure based on the time-reversal method. For some applications, setting transducers to retransmit at source locations is impracticable. Modeling a wave propagation path between two points using impulse response function is one way to overcome this limitation. This paper introduces alternative methods to calculate impulse response function, including an adaptive digital filter, deconvolution with singular value decomposition and Tikhonov regularization, and correlation. A discussion is also provided on the applicable frequency range and anti-noise ability of the impulse response functions obtained by all three techniques through simulation, and subsequently applies them to the designed time reversal process to enhance the signal-to-noise ratio (SNR) and restore source signals through experimentation. The conclusions of this study are given based on the level of accuracy using the SNR and correlation coefficient as indicators, and the computation time required by alternative methods is also an important factor to be discussed for real-time system design. Results prove that the proposed passive time reversal process is capable of enhancing the SNR and restoring the source signal. The alternative methods of calculating the impulse response function offer various advantages, and should be selected according to the application. If the time-cost is the first consideration and there is no dominant noise source, then correlation is the best choice for calculating impulse response function. If completeness of the reconstructed signal is the key point, the optimal deconvolution process is appropriate. If noise reduction is the highest priority in extracting a useful signal from noisy environments while ensuring acceptable restoration capability and computation time, an adaptive digital filter is suitable.

In this review paper, the use of the Time Reversal (TR) method as a computational tool for solving some classes of inverse problems is surveyed. The basics of computational TR are explained, using the scalar wave equation as a simple model. The application of TR to various problems in acoustics and elastodynamics is reviewed, in a selective and biased way as it leans on the author's personal view, referring to representative articles published on the subject.

Time reversal is a powerful procedure in application fields involving wave propagation. It is based on the invariance of the wave equations, in the absence of dissipation, in the time direction. This allows going backward in time to recover past events. We use time reversal to recover the location of a source applied at the initial time based on measurements at a later time. We generalize the procedure previously developed for the scalar wave equation¹ to elastodynamics. We show that the technique is quite robust, sometimes even in the presence of very high noise levels. Also it is not very sensitive to the medium characterizations, when a sufficient amount of measurement data is available. We extend previous work to get good refocusing for multiple sources. We introduce a new score to assess the quality of the numerical solution for the refocusing problem which produces good results. Furthermore, we use the refocusing technique as a basis for scatterer location recovery. By adding noise in a controlled manner we improve the scheme of finding the location of the scatterer.

We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows us to construct an approximate martingale for the phase space Wigner transform of two wave fields. Using a prioriL²-bounds available in the time-reversal setting, we prove that the Wigner transform in the high frequency limit converges in probability to its deterministic limit, which is the solution of a transport equation.

A novel method to perform a direct T (or CPT) symmetry test in the neutral kaon system is presented. This is based on the comparison of suitable transition probabilities, where the required interchange of in ↔ out states for a given process is obtained exploiting the Einstein-Podolsky-Rosen correlations of neutral kaon pairs produced at a ϕ-factory.

The possibility to perform these tests with the KLOE-2 experiment at DAΦNE, the Frascati ϕ-factory, is also briefly discussed.

The convective wave equation deals with wave propagation in a moving media. We focus on the underwater acoustic wave equation where the convective element is the flow of water inside a river, along its length. The main thrust of this paper is the ill-posed “refocusing” problem. The initial condition simulates an explosion in a small compact region and the response is recorded over time at several microphones. Having only partial and noisy information we expect that small perturbations will destroy the ability to recover the complete initial data. We use the time reversal (TR) technique to determine the location of the original explosion, given limited spatial observations. We test the effectiveness of this scheme under conditions including dissipation, dispersion, etc. We use finite differences and implement absorbing boundary conditions to simulate an unbounded region.

The paper falls into the category of computational methods for inverse scattering techniques for the identification of scatterers. We consider a linear elastodynamic problem and compare two popular methods for identifying a scatterer in the domain. Finite elements are employed with each of the two methods for spatial discretization. One method considered is Full Waveform Inversion using a gradient-based optimization and the adjoint method. In the adjoint procedure for calculating the gradient, we use the variant of discretizing the unknown parameters from the outset while all other variables remain continuous. Gradient optimization is performed in the examples using a quasi-Newton method. The other method compared is the computational Time Reversal technique, which is used in combination with an augmentation procedure to enhance performance. advantages and limitations of the two methods are outlined, and their performance is compared through an example from geophysics.

The time reversal of a completely-positive, non-equilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition mechanisms, and their role for relative entropy dynamics is discussed.