Classical and Quantum Statistical Physics

Statistical physics examines the collective properties of large ensembles of particles, and is a powerful theoretical tool with important applications across many different scientific disciplines. This book provides a detailed introduction to classical and quantum statistical physics, including links to topics at the frontiers of current research. The first part of the book introduces classical ensembles, provides an extensive review of quantum mechanics, and explains how their combination leads directly to the theory of Bose and Fermi gases. This allows a detailed analysis of the quantum properties of matter, and introduces the exotic features of vacuum fluctuations. The second part discusses more advanced topics such as the two-dimensional Ising model and quantum spin chains. This modern text is ideal for advanced undergraduate and graduate students interested in the role of statistical physics in current research. 140 homework problems reinforce key concepts and further develop readers' understanding of the subject.

Dipole Moment and Pressure Dependent Interlayer Excitons in MoSSe/WSSe Heterostructures

The broken mirror symmetry of the two-dimensional (2D) Janus material brings novel quantum properties and various application prospects. Particularly, when stacking into heterostructure, its intrinsic dipole moments and large band...

GEOMETRY OPTIMIZATION OF COUPLING ALLIN -METFORMIN USING DFT/B3LYP MOLECULAR MODELLING TECHNIQUE

This researchpaper includes the incorporation of Alliin at various energy levels and angles With Metformin using Gaussian 09 and Gaussian view 06. Two computers were used in this work. Samples were generated to draw, integrate, simulate and measure the value of the potential energy surface by means of which the lowest energy value was (-1227.408au). The best correlation compound was achieved between Alliin and Metformin through the low energy values where the best place for metformin to bind was through (CH2-). This is considered to be very useful for the industrial application of drugs. This level of calculation was used for physical and quantum properties such as total energy, HOMO and LUMO orbitals energies, and power gap. Besides, the calculation of FT-IR spectra in the range 400-4000 cm-1 was calculated in addition to the essential vibrational frequencies and the intensity of the vibrational bands. Moreover, the chemical displacement of the 1H and 13C NMR of the compound in the ground state was studied.

Dynamics of the Cavity Radiation of a Correlated Emis-sion Laser Coupled to a Two-Mode Thermal Reservoir

In this paper, the quantum properties of the cavity light beam produced by a coherently driven nondegenerate three-level laser with an open cavity and coupled to a two-mode thermal reservoir are thoroughly analyzed. We have carried out our analysis by putting the noise operators associated with the thermal reservoir in normal order. Here we discussed more the effect of thermal light and the spontaneous emission on the dynamics of the quantum processes. It is found that the maximum degree of intracavity squeezing 43% below the vacuum-state level. Moreover, the presence of thermal light leads to decrease the degree of entanglement.

Quantum cloud theory: Collapse expectations and superposition conservation

Most of metabolic processes are extremely complicated but occur spontaneously and steadily, the essential reason of which may be either a thermodynamic problem or related to some quantum properties. Here, collapse selection is interpreted with an analytical model of energy transfer, from which the concept of quantum cloud is defined as that during undetectable changes of a group of particles between its effective changes, particles are in the superposition of various energy states and the group is named as a cloud. It is deduced from a conservation notion of matter proportions that active cloud collapses have least-time expectation while passive collapses have matter-proportion expectation. As the results, quantum Zeno effect is a typical phenomenon of passive collapses while anti-Zeno effect is typical active collapses; moreover, the phenomenon of dark matter may be dark-cloud effect of normal matter while the phenomenon of accelerating universe may be induced by the luminescent asymmetries of bright celestial bodies.

Quantum properties near the instability boundary in optomechanical system

The properties of the system near the instability boundary are very sensitive to external disturbances, which is important for amplifying some physical effects or improving the sensing accuracy. In this paper, the quantum properties near the instability boundary in a simple optomechanical system has been studied by numerical simulations. Calculations show that the transitional region connecting the Gaussian states and the Ring states when crossing the boundary is sometimes different from the region centered on the boundary line, but it is more essential. The change of the mechanical Wigner function in the transitional region directly reflects its bifurcation behavior in classical dynamics. Besides, quantum properties such as mechanical second-order coherence function and optomechanical entanglement, can be used to judge the corresponding bifurcation types and estimate the parameter width and position of the transitional region. The non-Gaussian transitional states exhibit strong entanglement robustness, and the transitional region as a boundary ribbon can be expected to replace the original classical instability boundary line in future applications.

Photon counting statistics with imperfect detectors

Measurement of photon statistics is an important tool for the verification of quantum properties of light. Due to the various imperfections of real single photon detectors, the observed statistics of photon counts deviates from the underlying statistics of photons. Here we analyze statistical properties of coherent states, and investigate a connection between Poissonian distribution of photons and sub-Poissonian distribution of photon counts due to the detector dead-time corrections. We derive a functional dependence between the mean number of photons and the mean number of photon counts, as well as connection between higher-order statistical moments, for the pulsed or continuous wave coherent light sources, and confirm the results by numerical simulations.

Ergotropy from quantum and classical correlations

It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present analysis, we show that the ergotropy can be expressed as a function of the quantum mutual information, which demonstrates the contributions to the extractable work from classical and quantum correlations. More specifically, we analyze bipartite quantum systems with locally thermal states, such that the only contribution to the ergotropy originates in the correlations. Our findings are illustrated for a two-qubit system collectively coupled to a thermal bath.

Barrier billiard and random matrices

The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular billiard with a barrier in the centre can be reduced to the investigation of a certain unitary matrix. Under heuristic assumptions this matrix is substituted by a special low-complexity random unitary matrix of independent interest. The main results of the paper are (i) spectral statistics of such billiards is insensitive to the barrier height and (ii) it is well described by the semi-Poisson distributions.

Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States

Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal pure states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two mixed states.