Statistical-Mechanical Entropy of a Black Hole with a Global Monopole to All Orders in Planck Length

Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle, we calculate the statistical entropy of the scalar field in the global monopole black hole spacetime without any artificial cutoff. It is shown that the entropy is proportional to the horizon area.     

Entropy of Four-Dimensional Spherically Symmetric Black Holes with Planck Length

Considering corrections to all orders in Planck length on the quantum state density from a generalized uncertainty principle （GUP）, we calculate the statistical entropy of the Bose field and Fermi field on the background of the four-dimensional spherically symmetric black holes without any cutoff. It is obtained that the statistical entropy is directly proportional to the area of horizon.     

Entropy of the rotating and charged black string to all orders in the Planck length

<正>By using the entanglement entropy method,this paper calculates the statistical entropy of the Bose and Fermi fields in thin films,and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string.Here,the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string.Taking into account the effect of the generalized uncertainty principle on quantum state density,it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model.These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect.The ultraviolet cut-off in the brick-wall model is not reasonable.The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon.From the viewpoint of quantum statistical mechanics,the correction value of Bekenstein-Hawking entropy is obtained.This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.     

Horowitz-Strominger Black Hole Entropy Without Brick Wall

A Horowitz-Strominger black hole is discussed through a new equation of state density motivated by the gener-alized uncertainty relation in quantum gravity. There is no burst in the last stage of emission from a Horowitz-Strominger black hole. When the new equation of state density is used to investigate the entropy of bosonic fieldand fermionic field outside the horizon of a static Horowitz-Strominger black hole, the divergence that appearsin the brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derivedfrom the contribution in the vicinity of the horizon.     

Information entropy for static spherically symmetric black holes

By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein--Hawking entropy when the suitable cutoff factor is adopted.     

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function of bosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant A introduced in generalized uncertainty principle takes a proper value, we derive Bekenstein- Hawking entropy and the correction value corresponding cosmologicaJ horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small mass approximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropy of the black string cosmological horizon in non-spherical coordinate spacetime.     

Shannon information entropies for rectangular multiple quantum well systems with constant total lengths

We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum(FWHM) of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki(BBM)inequality.     

Thermodynamics of Phase Transitions of a Kerr Nonlinear Blackbody

We study the thermodynamics of phase transitions of a blackbody whose interior is filled by a Kerr nonlinear crystal. There is a transition temperature To, above which the Kerr nonlinear blackbody is in the normal thermal radiation state, and below which it is in the squeezed thermal radiation state. At To, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the squeezed thermal radiation state.     

Block Entanglement in the Single-Hole Hubbard Model

We investigate the distribution of the entanglement of the one-dimensional single-hole Hubbard model （HM） and study the relationship between the entanglement and quantum phase transition in the model. The von Neumann entropy of a block with neighbouring spins L for a single-hole HM is calculated using the densitymatrix renormalization group. The distributions of the entanglement entropy in the ground state, as a function of block length, show a dramatic effect, i.e. effectively decoupling with the centres, no matter how the Coulomb interaction u 〉0 or u 〈0. Contrarily, for the Coulomb interaction u = 0 or close to zero, the entanglement entropy in the single-hole model reaches a saturation value for a certain block size. For a fixed size L = 40, the ground state entanglement entropy measure, as a function of u1 shows a peak corresponding to the critical quantum phase transition.     

Temperature Effects of Parabolic Linear Bound Potential and Coulomb Bound Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong coupling in a parabolic quantum dot, we obtain the eigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method of Pekar type. This system in a quantum dot may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground state and the first-excited state, we obtain the time evolution of the electron density. The relations of the probability density of electron on the temperature and the electron-LO-phonon coupling constant and the relations of the period of oscillation on the temperature, the electron-LO-phonon coupling constant, the Coulomb binding parameter and the confinement length are derived. The results show that the probability density of electron oscillates with a period when the electron is in the superposition state of the ground and the first-excited state, and show that there are different laws that the probability density of electron and the period of oscillation change with the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher. And it is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases with increasing the confinement length not only at lower temperatures but also at higher temperatures.     

Entropy squeezing of the field interacting with a nearly degenerate V-type three-level atom

The position- and momentum-entopic squeezing properties of the optical field in the system of a nearly degenerate three-level atom interacting with a single-mode field are investigated. Calculation results indicate that when the field is initially in the vacuum state, it may lead to squeezing of the position entropy or the momentum entropy of the field if the atom is prepared properly. The effects of initial atomic state and the splitting of the excited levels of the atom on field entropies are discussed in this case. When the initial field is in a coherent state, we find that position-entropy squeezing of the field is present even if the atom is prepared in the ground state. By comparing the variance squeezing and entropy squeezing of the field we confirm that entropy is more sensitive than variance in measuring quantum fluctuations.     

Properties of Parabolic Linear Bound Potential and Coulomb Bound Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong-coupling in a parabolic quantum dot, we obtain the eigenenergy of the ground-state and the first-excited state, the eigenfunctions of the ground-state and the first-excited state by using variational method of Pekar type. This system in quantum dot may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground- and the first-excited state, we obtain the time evolution of the electron density. The relation of the probability density of electron on the Coulomb binding parameter and the relations of the period of oscillation on the Coulomb binding parameter, the electron-LO-phonon coupling constant and the confinement length are derived.     

The influence of electric field on a parabolic quantum dot qubit

This paper calculates the time evolution of the quantum mechanical state of an electron by using variational method of Pekar type on the condition of electric--LO-phonon strong coupling in a parabolic quantum dot. It obtains the eigenenergies of the ground state and the first-excited state, the eigenfunctions of the ground state and the first-excited state This system in a quantum dot may be employed as a two-level quantum system qubit. The superposition state electron density oscillates in the quantum dot with a period when the electron is in the superposition state of the ground and the first-excited state. It studies the influence of the electric field on the eigenenergies of the ground state, the first-excited state and the period of oscillation at the different electron--LO-phonon coupling constant and the different confinement length.     

Black Hole Entropy with Modified Dispersion Relations

There is much interest in resolving the quantum corrections to Bekenstein-Hawking entropy with a large length scale limit. The leading correction term ＆ given by the logarithm of black hole area with a model-dependent coefficient. Recently the research for quantum gravity implies the emergence of a modification of the energy-momentum dispersion relation （MDR）, which plays an important role in the modified black hole thermodynamics. In this paper, we investigate the quantum corrections to Bekenstein-Hawking entropy in four-dimensional Sehwarzschild black hole and Reissner-Nordstrom black hole respectively based on MDR.     

Quantum Mechanical Nature in Liquid NMR Quantum Computing

The quantum nature of bulk ensemble NMR quantum computing-the center of recent heated debate,is addressed.Concepts of the mixed state and entanglement are examined,and the data in a two-qubit liquid NMR quantum computation are analyzed.the main points in this paper are;i) Density matrix describes the “state“ of an average particle in an ensemble.It does not describe the state of an individual particle in an ensemble;ii) Entanglement is a property of the wave function of a microscopic particle(such as a molecule in a liquid NMR sample),and separability of the density matrix canot be used to measure the entanglement of mixed ensemble;iii) The state evolution in bulkensemble NMR quantum computation is quantum-mechanical;iv) The coefficient before the effective pure state density matrix,ε,is a measure of the simultaneity of the molecules in an ensemble,It reflets the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system.The decomposition of the density matrix into product states is only an indication that the ensemble can be prepared by an ensemble with the particles unentangeld.We conclude that effective-pure-state NMR quantum computation is genuine,not just classical simulations.     

Brick Walls for Nonstationary Black Holes

The validity condition of the brick-wall model is analysed in nonstationary space-time.It is shown that the model holds only in thin regions,only by using tortoise coordinates near the event horizon of a slowly varying(quasistationary)black hole.The reason for the use of tortoise cooridnates is that the stationary state solutions of quantum field equations in other coordinates do not exist for any region in nonstationary space-time.Meanwhile,the quantum corrections to the entropy of the Vaidya-Bonner black hole due to the spin fields are calculated in terms of the brick-wall model.     

Boundary Quantum Entanglement of the XXZ Spin Chain with Boundary Impurities

The boundary quantum entanglement for the s = 1/2 X X Z spin chain with boundary impurities is studied via the density matrix renormalization group （DMRG） method. It is shown that the entanglement entropy of the boundary bond （the impurity and the chain spin next to it） behaves differently in different phases. The relationship between the singular points of the boundary entropy and boundary quantum critical points is discussed.     

Quantum confinement and surface chemistry of 0.8–1.6 nm hydrosilylated silicon nanocrystals

In the framework of density functional theory(DFT), we have studied the electronic properties of alkene/alkynehydrosilylated silicon nanocrystals(Si NCs) in the size range from 0.8 nm to 1.6 nm. Among the alkenes with all kinds of functional groups considered in this work, only those containing –NH2and –C4H3S lead to significant hydrosilylationinduced changes in the gap between the highest occupied molecular orbital(HOMO) and the lowest unoccupied molecular orbital(LUMO) of an Si NC at the ground state. The quantum confinement effect is dominant for all of the alkenehydrosilylated Si NCs at the ground state. At the excited state, the prevailing effect of surface chemistry only occurs at the smallest(0.8 nm) Si NCs hydrosilylated with alkenes containing –NH2and –C4H3S. Although the alkyne hydrosilylation gives rise to a more significant surface chemistry effect than alkene hydrosilylation, the quantum confinement effect remains dominant for alkyne-hydrosilylated Si NCs at the ground state. However, at the excited state, the effect of surface chemistry induced by the hydrosilylation with conjugated alkynes is strong enough to prevail over that of quantum confinement.     

Entanglement swapping of continuous variable using squeezed vacuum states

We present a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the von Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.     

Symmetry and size effects on energy and entanglement of an exciton in coupled quantum dots

We study theoretically the essential properties of an exciton in vertically coupled Gaussian quantum dots in the presence of an external magnetic field. The ground state energy of a heavy-hole exciton is split into four energy levels due to the Zeeman effect. For the symmetrical system, the entanglement entropy of the exciton state can reach a value of 1. However, for a system with broken symmetry, it is close to zero. Our results are in good agreement with previous studies.