Excited state quantum phase transitions in many-body systems

Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean-field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions.     

Periodic trajectories in the Hilbert space and generalized semi-classical bound states of many-body systems

Using a stationary phase approximation to calculate a functional integral defined on continuous overcomplete sets of vectors of the Hilbert space, one derives a generalized semi-classical quantization condition for periodic trajectories in the Hilbert space. This quantization condition is interpreted in terms of a variational principle. Application to the time dependent Hartree—Fock approximation is presented.     

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r ₁₂, r ₁₃, r ₁₄, r ₂₃, r ₂₄, r ₃₄) and ten (r ₁₂, r ₁₃, r ₁₄, r ₁₅, r ₂₃, r ₂₄, r ₂₅, r ₃₄, r ₃₅ and r ₄₅) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial wave functions for the ¹ S states in four-electron atomic systems include the two independent spin functions χ₁ = αβαβ + βαβα − βααβ − αββα and χ₂ = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited 2³ S states in four- electron atomic systems.     

The ultrasound application does not affect to the thermal properties and chemical composition of virgin olive oils

In this work, the effects of high power ultrasound treatment (40 kHz) on virgin olive oil (VOO) for different times (0, 15, 30 min) were studied, in order to verify if extent modifications in their chemical composition and thermal properties. The effects of the different ultrasound treatments on VOOs were determined considering the following parameters: quality index (free acidity, K₂₃₂ and K₂₇₀), lipid profile (fatty acids and triglycerides composition) minor components (phenols, tocopherols, pigments and volatiles) and thermal properties (crystallization and melting) by Differential Scanning Calorimetry (DSC).During the ultrasound treatments, bubbles growth was present in the VOO due to the phenomenon of cavitation and a slight increase of the temperature was observed. In general, the ultrasound treatments did not cause alterations on VOO parameters evaluated (oxidation state, lipid profile, minor components and thermal profiles). However, a slight decrease was observed in some volatile compounds.     

Characterizing and quantifying frustration in quantum many-body systems

We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.     

Range of forces and broken symmetries in many-body systems

It is argued that for a many-body system with short range forces the commutators between local operators at different times will be fast decreasing for large spatial separations.This allows the adaptation of many discussions in relativistic field theories to the case of a many-body system with short range forces. In particular one has the result that a spontaneous breakdown in symmetry implies the existence of excitations of arbitrarily small energy. However this result has essentially only one application: We know that the Galilei invariance is always broken (in a medium of finite density). Therefore one concludes that in a many-body system with short range forces there can never be an energy gap.Supported by the National Science Foundation.     

Symmetry breaking and finite-size effects in quantum many-body systems

We consider a quantum many-body system on a lattice which exhibits a spontaneous symmetry breaking in its infinite-volume ground states, but in which the corresponding order operator does not commute with the Hamiltonian. Typical examples are the Heisenberg antiferromagnet with a Néel order and the Hubbard model with a (superconducting) off-diagonal long-range order. In the corresponding finite system, the symmetry breaking is usually obscured by quantum fluctuation and one gets a symmetric ground state with a long-range order. In such a situation, Horsch and von der Linden proved that the finite system has a low-lying eigenstate whose excitation energy is not more than of orderN ^–1, whereN denotes the number of sites in the lattice. Here we study the situation where the broken symmetry is a continuous one. For a particular set of states (which are orthogonal to the ground state and with each other), we prove bounds for their energy expectation values. The bounds establish that there exist ever-increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant timesN ^–1. A crucial feature of the particular low-lying states we consider is that they can be regarded as finite-volume counterparts of the infinite-volume ground states. By forming linear combinations of these low-lying states and the (finite-volume) ground state and by taking infinite-volume limits, we construct infinite-volume ground states with explicit symmetry breaking. We conjecture that these infinite-volume ground states are ergodic, i.e., physically natural. Our general theorems not only shed light on the nature of symmetry breaking in quantum many-body systems, but also provide indispensable information for numerical approaches to these systems. We also discuss applications of our general results to a variety of interesting examples. The present paper is intended to be accessible to readers without background in mathematical approaches to quantum many-body systems.     

Majorana modes in solid state systems and its dynamics

We review the properties of Majorana fermions in particle physics and point out that Majorana modes in solid state systems are significantly different. The key reason is the concept of anti-particle in solid state systems is different from its counterpart in particle physics. We define Majorana modes as the eigenstates of Majorana operators and find that they can exist both at edges and in the bulk. According to our definition, only one single Majorana mode can exist in a system no matter at edges or in the bulk. Kitaev’s spinless p-wave superconductor is used to illustrate our results and the dynamical behavior of the Majorana modes.     

Ab-initio electronic and optical properties of low dimensional systems: From single particle to many-body approaches

Low dimensional systems, such as nanodots, nanotubes, nanowires, have attracted great interest in the last years, due to their possible application in nanodevices. It is hence very important to describe accurately their electronic and optical properties within highly reliable and efficient ab-initio approaches. Density functional theory (DFT) has become in the last 20 years the standard technique for studying the ground-state properties, but this method often shows significant deviations from the experiment when electronic excited states are involved. The use of many-body Green’s functions theory, with DFT calculations taken as the zero order approximation, is today the state-of-the-art technique for obtaining quasi-particle excitation energies and optical spectra. In this paper we will present the current status of this theoretical and computational approach, showing results for different kinds of low dimensional systems.     

Short-term exposure to a 1.5 tesla static magnetic field does not affect somato-sensory-evoked potentials in man

The literature is contradictory regarding the effect of static magnetic fields on the function of the central nervous system of mammals. Since human subjects are exposed to intense static magnetic fields during magnetic resonance imaging, it is important to determine if the static magnetic field adversely affects the nervous system of man. Therefore, somato-sensory evoked potentials (SEPs) elicited from median nerve stimulation were measured in 11 normal subjects before and during short-term exposure to a 1.5 Tesla static magnetic field. Specially modified instrumentation was used to record SEPs that were unperturbed by the static magnetic field. There were no statistically significant differences in the N20 or P25 latencies or in the amplitude from N20 negative peak to P25 positive peak of the SEPs obtained before compared to those recorded during exposure to the static magnetic field. In addition, there were no changes in the waveforms associated with exposure to the static magnetic field. We conclude that short-term exposure to a 1.5 Tesla static magnetic field does not affect SEPs (i.e., nerve conduction and synaptic transmission were within normal limits) in normal human subjects.     

Recording a volume image on a wavelength which does not exist in the source of emission

A method for the volume image recording is described which uses a radiation correlation function module for the information carrier.     

退激发压缩真空态及其特性

利用退激发压缩真空态归一化函数的产生函数, 获得了归一化的退激发压缩真空态. 借助于此态的归一化常数和中介表象理论, 我们得到了退激发压缩真空态的量子Tomogram函数和一些新的数学公式.     

Flat-topped Mathieu-Gauss beam and its transformation by paraxial optical systems

In order to avoid the severe axial intensity oscillations which appear when an ideal Mathieu beam is truncated, we propose to modulate it by a flattened multi-Gaussian envelope. The obtained beam, which is referred as flattened Mathieu-Gauss (FTMG) beam, can be expanded into a finite series of Mathieu-Gauss beams with various waists. The propagation study of this beam reveals that the axial intensity is unchanged within a certain propagation distance as for super-Gaussian-Bessel beams or Gori’s flattened Bessel beams. By using Collins formula, we derive closed-form expressions of FTMG beam propagating through a paraxial axisymmetric ABCD optical system. Some numerical calculations and discussions are also given.     

Generalized Helmholtz-Gauss beam and its transformation by paraxial optical systems

We introduce the generalized Helmholtz-Gauss (gHzG) beam and analyze its propagation through optical systems described by ABCD matrices with real and complex elements. The transverse mathematical structure of the gHzG beam is form invariant under paraxial transformations and reduces to those of ordinary HzG and modified HzG beams as special cases. We derive a closed-form expression for the fractional Fourier transform of gHzG beams.     

Macroscopic atom-molecule dark state and its collective excitations in fermionic systems

We show that a robust macroscopic atom-molecule dark state can exist in fermionic systems, which represents a coherent superposition between the ground molecular Bose-Einstein condensates and the atomic BCS paired state. We take advantage of the tunability offered by external laser fields, and explore this superposition for demonstrating coherent oscillations between ground molecules and atom pairs. We interpret the oscillation frequencies in terms of the collective excitations of the dark state.     

Path-integral bosonization of a non-local interaction and its application to the study of 1d many-body systems

We extend the path-integral approach to bosonization to the case in which the fermionic interaction is non-local. In particular we obtain a completely bosonized version of a Thirring-like model with currents coupled by general (symmetric) bilocal potentials. The model contains the Tomonaga-Luttinger model as a special case; exploiting this fact we study the basic properties of the 1d spinless fermionic gas: fermionic correlators, the spectrum of collective modes, etc. Finally, we discuss the generalization of our procedure to the non-abelian case, thus providing a new tool to be used in the study of 1d many-body systems with spin-flipping interactions.     

Diagonal entropy in many-body systems: Volume effect and quantum phase transitions

We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbor interactions. We focus on the DE of a subsystem of L continuous spins. We show that the DE in many-body systems, regardless of integrability, can be represented as a volume term plus a logarithmic correction and a constant offset. Quantum phase transition points can be explicitly identified by the three coefficients thereof. Besides, by combining entanglement entropy and the relative entropy of quantum coherence, as two celebrated representatives of quantumness, we simply obtain the DE, which naturally has the potential to reveal the information of quantumness. More importantly, the DE is concerning only the diagonal form of the ground state reduced density matrix, making it feasible to measure in real experiments, and therefore it has immediate applications in demonstrating quantum supremacy on state-of-the-art quantum simulators.     

Positron bound systems in benzene and in naphthalene

Summary Positron decay in liquid naphthalene and benzene was investigated through measurements of lifetimes and magnetic quenching. The obtained results when compared with those already known in solid phase suggest that positrons become bound in two different systems. The first has a lifetime τ₃≈1 ns which is unaffected by the melting, while the second (τ₄≈3 ns) arises above melting and behaves as a relaxed positronium. This work was supported by CISM (Centro Interuniversitario di Struttura della Materia) del Ministero della Pubblica Istruzione, and by GNSM (Gruppo Nazionale di Struttura della Materia) del CNR.