Unitary equilibrations: probability distribution of the Loschmidt echo

Closed quantum systems evolve unitarily and therefore cannot converge in a strong sense to an equilibrium state starting out from a generic pure state. Nevertheless for large system size one observes temporal typicality. Namely, for the overwhelming majority of the time instants, the statistics of observables is practically indistinguishable from an effective equilibrium one. In this paper we consider the Loschmidt echo (LE) to study this sort of unitary equilibration after a quench. We draw several conclusions on general grounds and on the basis of an exactly-solvable example of a quasi-free system. In particular we focus on the whole probability distribution of observing a given value of the LE after waiting a long time. Depending on the interplay between the initial state and the quench Hamiltonian, we find different regimes reflecting different equilibration dynamics. When the perturbation is small and the system is away from criticality the probability distribution is Gaussian. However close to criticality the distribution function approaches a double peaked, "batman-hood" shaped, universal form.Comment: 15 pages, 16 figure

Entanglement susceptibility: Area laws and beyond

Generic quantum states in the Hilbert space of a many body system are nearly maximally entangled whereas low energy physical states are not; the so-called area laws for quantum entanglement are widespread. In this paper we introduce the novel concept of entanglement susceptibility by expanding the 2-Renyi entropy in the boundary couplings. We show how this concept leads to the emergence of area laws for bi-partite quantum entanglement in systems ruled by local gapped Hamiltonians. Entanglement susceptibility also captures quantitatively which violations one should expect when the system becomes gapless. We also discuss an exact series expansion of the 2-Renyi entanglement entropy in terms of connected correlation functions of a boundary term. This is obtained by identifying Renyi entropy with ground state fidelity in a doubled and twisted theory.Comment: minor corrections, references adde

Exact infinite-time statistics of the Loschmidt echo for a quantum quench

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasi-critical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.Comment: 4 pages, 2 figure

Structural changes of tissue samples exposed to low frequency electromagnetic field: A FT-IR absorbance study

In the present work, we report on a preliminary Fourier Transform Infrared (FT-IR) Absorbance study performed on different kind of rat tissues, such as kidney and heart, exposed to a "non-ionizing" radiation source at low frequency, in the range typical of micro-waves (300 MHz <v< 300 GHz). The data were collected in a wide wavenumber region, from 400 cm−1to 4000 cm−1. The comparison of the absorbance spectra in the case of the normal tissues with the irradiated ones has shown significant differences in the spectral features in accordance with the morphological analysis performed by the optical microscopy

Geology and geophysics at the archeological park of Vulci

The Vulci archeological site was object of interest by the Soprinten- denza ai beni culturali dell’Etruria meridionale (Italian government department responsible for southern Etruria’s cultural heritage) since the beginning of the 20th century. In 2001, the Ministero dei Beni Cul- turali (Italian ministry of cultural heritage) along with the local au- thorities, opened a natural-archeological park. In this area, it lies most of the ancient Etruscan city of Velch (today known by its Latin name, Vulci) including the Osteria Necropolis that is the object of this study. Recently, new archaeological excavations were made and the local au- thorities needed major geological information about the volcanic litho- types where the Etruscans used to build their necropolis. The aim of this study is to define the geological and geophysical characteristics of the rock lithotypes present in the Vulci park. For this purpose, a geo- logical map of the area (1:10000) has been realized. Moreover, two dif- ferent geophysical methods were applied: measurements of magnetic susceptibility and electrical resistivity tomography. Magnetic suscep- tibility analyses clearly identify magnetic contrasts between different lithotypes; the characteristics of the pyroclastic flow that originated the Sorano unit 2 and its vertical facies variations are well recorded by this parameter that along with lithostratigraphic observations provides information about the depositional conditions. Two electrical resistiv- ity tomographies were performed, which show the Sorano unit 2 thick- ness to be of c. 7 m with resistivity values ranging from 200 to 400 Ω·m. This kind of multidisciplinary approach resulted to be suitable to study this type of archaeological sites, revealing that areas charac- terized by a relevant thickness and wide areal extension of volcanic lithotypes can be a potential site where Etruscans might have excavated their necropolis

Fidelity approach to quantum phase transitions

We review briefly the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin-Meshkov-Glick model, are introduced at the graduate-student level. In addition, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.Comment: 41 pages, 31 figures. We apologize if we omit acknowledging your relevant works. Do tell. An updated version with clearer figures can be found at: http://www.phy.cuhk.edu.hk/~sjgu/fidelitynote.pd

Combining Raman and infrared spectroscopy as a powerful tool for the structural elucidation of cyclodextrin-based polymeric hydrogels

A detailed experimental and theoretical vibrational analysis of hydrogels of b-cyclodextrin nanosponges (b-CDNS), obtained by polymerization of b-cyclodextrin (b-CD) with the cross-linking agent ethylenediaminetetraacetic acid (EDTA), is reported here. Thorough structural characterization is achieved by exploiting the complementary selection rules of FTIR-ATR and Raman spectroscopies and by supporting the spectral assignments by DFT calculations of the spectral profiles. The combined analysis of the FTIR-ATR spectra of the polymers hydrated with H2O and D2O allowed us to isolate the HOH bending of water molecules not involved in symmetrical, tetrahedral environments. The analysis of the HOH bending mode was carried out as a function of temperature, showing the existence of a supercooled state of the water molecules. The highest level of cooperativity of the hydrogen bond scheme was reached at a value of the b-CD/EDTA molar ratio n = 6. Finally, the connectivity pattern of ‘‘uncoupled’’ water molecules bound to the nanosponge backbone was found to be weakened by increasing T. The temperature above which the population of non-tetracoordinated water molecules becomes predominant turned out to be independent of the parameter n

Spectroscopy 16 (2002) 245-250 245 IOS Press Recent results on biomedical problems: A Fourier transform infrared (FT-IR) study

Abstract. In the present work, we report on a vibrational study performed on rat encephalon samples and on human tissue affected by cancer, using Fourier Transform Infrared absorbance spectroscopy. As the brain rat tissue is concerned, the FT-IR measurements, performed in the CH-OH vibrational stretching region (2400-3800 cm −1 ), permitted us to reveal the presence of a very diffuse commercial benzodiazepine: VALIUM R . The comparison between the spectral features of normal brain and the ones of samples with administrated substance has unambiguously showed that the CH stretching region seems not to be affected by any change for the pharmacological treatment, instead the OH band is strongly modified probably due to the presence of a new spectral contribution characteristic of diazepam molecule. In the case of skin tissue the investigation was addressed to characterize the presence of two different pathologies, namely epithelioma and basalioma, and to show clear different spectral features passing from the normal tissue to the malignant one in particular in the region (1500-2000 cm −1 ) which is typical of the lipids vibrational bands

Renormalization of the vacuum angle in quantum mechanics, Berry phase and continuous measurements

The vacuum angle $\theta$ renormalization is studied for a toy model of a quantum particle moving around a ring, threaded by a magnetic flux $\theta$. Different renormalization group (RG) procedures lead to the same generic RG flow diagram, similar to that of the quantum Hall effect. We argue that the renormalized value of the vacuum angle may be observed if the particle's position is measured with finite accuracy or coupled to additional slow variable, which can be viewed as a coordinate of a second (heavy) particle on the ring. In this case the renormalized $\theta$ appears as a magnetic flux this heavy particle sees, or the Berry phase, associated with its slow rotation.Comment: 4 pages, 2 figure