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Register a new userThermalized non-equilibrated matter and high temperature superconducting state in quantum many-body systems
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A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relaxation--equilibration, a phase memory of the way the many-body system was excited remains. As an example, we analyze data on a strong forward peaking of thermal proton yield in the Bi($gamma$,p) photonuclear reaction. New analysis shows that the phase relaxation in highly-excited heavy nuclei can be 8 orders of magnitude or even much longer than the energy relaxation. We argue that thermalized non-equilibrated matter resembles a high temperature superconducting state in quantum many-body systems. We briefly present results on the time-dependent correlation function of the many-particle density fluctuations for such a superconducting state. It should be of interest to experimentally search for manifestations of thermalized non-equilibrated matter in many-body mesoscopic systems and nanostructures.
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A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relaxation (thermalization), a phase memory of the way the strongly interacting many-body system was excited remains. In this contribution we analyze a low energy evaporating proton data in nucleon induced reactions at $simeq$62 MeV incident energy with $^{197}$Au, $^{208}$Pb, $^{209}$Bi and $^{nat}$U. Our analysis demonstrates that the thermalized non-equilibrated matter survives a cascade of several evaporating particles. Thus the experiments show that the effect of the anomalously slow phase relaxation, with upper limits of the phase relaxation widths in the range 1-10$^{-4}$ eV, is stable with respect to the multi-step evaporating cascade from the thermalized compound nuclei. We also briefly mention manifestations and implications of the thermalized non-equilibrated matter for some other fields.
We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some landmarks within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as is the system in state A or state B?. In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number $n$ of identical copies of the system, and estimate the expected error as $n$ becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.
The idea of a thermalized non-equilibrated state of matter offers a conceptually new understanding of the strong angular asymmetry. In this compact review we present some clarifications, corrections and further developments of the approach, and provide a brief account of results previously discussed but not reported in the literature. The cross symmetry compound nucleus $S$-matrix correlations are obtained (i) starting from the unitary $S$-matrix representation, (ii) by explicitly taking into account a process of energy equilibration, and (iii) without taking the thermodynamic limit of an infinite number of particles in the thermalized system. It is conjectured that the long phase memory is due to the exponentially small total spin off-diagonal resonance intensity correlations. This manifestly implies that the strong angular asymmetry intimately relates to extremely small deviations of the eigenfunction distribution from Gaussian law. The spin diagonal resonance intensity correlations determine a new time/energy scale for a validity of random matrix theory. Its definition does not involve overlaps of the many-body interacting configurations with shell model non-interacting states and thus is conceptually different from the physical meaning (inverse energy relaxation time) of the spreading widths introduced by Wigner. Exact Gaussian distribution of the resonance wave functions corresponds to the instantaneous phase relaxation. We invite the nuclear reaction community for the competition to describe, as the first challenge, the strong forward peaking in the typically evaporation part of the proton spectra. This is necessary to initiate revealing long-term misconduct in the heavily cross-disciplinary field, also important for nuclear industry applications.
We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local measurements. We show that average frustration properties are completely determined by the behavior of the maximally mixed ground state. We identify sufficient conditions for a quantum spin system to saturate the bound, and for models with twofold degeneracy we prove that average and local frustration coincide.
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