Hawking radiation of <Emphasis Type="Italic">E</Emphasis> < <Emphasis Type="Italic">m</Emphasis> massive particles in the tunneling formalism

We use the tunneling formalism to calculate the Hawking radiation of massive particles. For E ≥ m, we recover the traditional result, identical to the massless case. But E < m particles can also tunnel across the horizon in a Hawking process. We study the probability for detecting such E < m particles as a function of the distance from the horizon and the energy of the particle in the tunneling formalism. We derive a general formula and obtain simple approximations in the near-horizon limit and in the limit of large radii.     

Photoionization of argon, krypton and xenon clusters in the inner valence shell region

Photoionization of rare gas clusters in the innervalence shell region has been investigated using threshold photoelectron and photoion spectrometers and synchrotron radiation. Two classes of states are found to play an important role: (A) valence states, correlated to dissociation limits involving an ion with a hole in its innervalence ns shell, (B) Rydberg states correlated to dissociation limits involving an ion with a hole in its outervalence np shell plus an excited neutral atom. In dimers, class A states are “bright”, that is, accessible by photoionization, and serve as an entrance step to form the class B “dark” states; this character fades as the size of the cluster increases. In the dimer, the “Mulliken” valence state is found to present a shallow potential well housing a few vibrational levels; it is predissociated by the class B Rydberg states. During the predissociation a remarkable energy transfer process is observed from the excited ion that loses its innershell electron to its neutral partner. Received: 10 February 1998 / Revised: 17 July 1998 / Accepted: 31 July 1998     

Thermodynamics Properties of the Inner Horizon of?a?Kerr-Newman Black Hole

In this paper, we study the thermal properties of the inner horizon of a Kerr-Newman black hole. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a Kerr-Newman black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. The cut-off factor is same as it in calculation of the entropy of the outer horizon, 90β. In addition, we write the integral and differential Bekenstein-Smarr formula as the parameters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, We calculate the tunneling rate of the outer horizon Γ₊ and the inner horizon Γ₋. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ₊⋅Γ₋. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (ΔS _BH ), and there is no information loss.     

Tunneling Effect of Two Horizons from a Reissner-Nordstrom Black Hole

The understanding of possible role played by the inner horizon of black holes in black hole thermodynamics is still somewhat incomplete. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a R-N black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. In addition, the cut-off factor is 90β, which is same in calculation of the entropy of the outer horizon. So, we prove the existence of thermal characters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, we study the tunneling effect including the inner horizon of the Reissner-Nordstrom black hole. We calculate the tunneling rate of the outer horizon Γ₊ and the inner horizon Γ₋. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ₊⋅Γ₋. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (ΔS _BH ), and there is no information loss.     

Fuzzball solutions for black holes and D1-brane-D5-brane microstates

We revisit the relation between fuzzball solutions and D1-brane-D5-brane microstates. A consequence of the fact that the R ground states (in the usual basis) are eigenstates of the R charge is that only neutral operators can have nonvanishing expectation values on these states. We compute the holographic 1-point functions of the fuzzball solutions and find that charged chiral primaries have nonzero expectation values, except when the curve characterizing the solution is circular. The nonzero vacuum expectation values reflect the fact that a generic curve breaks R symmetry completely. This implies that fuzzball solutions (excepting circular ones) can only correspond to superpositions of R states and we give a proposal for the superposition corresponding to a given curve. We also address the question of what would be the geometric dual of a given R ground state.     

Black holes and beyond

The black hole information paradox forces us into a strange situation: we must find a way to break the semiclassical approximation in a domain where no quantum gravity effects would normally be expected. Traditional quantizations of gravity do not exhibit any such breakdown, and this forces us into a difficult corner: either we must give up quantum mechanics or we must accept the existence of troublesome ‘remnants’. In string theory, however, the fundamental quanta are extended objects, and it turns out that the bound states of such objects acquire a size that grows with the number of quanta in the bound state. The interior of the black hole gets completely altered to a ‘fuzzball’ structure, and information is able to escape in radiation from the hole. The semiclassical approximation can break at macroscopic scales due to the large entropy of the hole: the measure in the path integral competes with the classical action, instead of giving a subleading correction. Putting this picture of black hole microstates together with ideas about entangled states leads to a natural set of conjectures on many long-standing questions in gravity: the significance of Rindler and de Sitter entropies, the notion of black hole complementarity, and the fate of an observer falling into a black hole.     

Instability of black hole horizon with respect to electromagnetic excitations

Analyzing exact solutions of the Einstein–Maxwell equations in the Kerr–Schild formalism we show that black hole horizon is instable with respect to electromagnetic excitations. Contrary to perturbative smooth harmonic solutions, the exact solutions for electromagnetic excitations on the Kerr background are accompanied by singular beams which have very strong back reaction to metric and break the horizon, forming the holes which allow radiation to escape interior of black-hole. As a result, even the weak vacuum fluctuations break the horizon topologically, covering it by a set of fluctuating microholes. We conclude with a series of nontrivial consequences, one of which is that there is no information loss inside of black-hole.     

Correction to Entropy of Schwarzschild Black Hole by Modified Dispersion Relation

Taking WKB approximation to solve the scalar field equation in the Schwarzschild black hole spacetime, we can get the classical momenta. Substituting the classical momenta into state density equation corrected by the modified dispersion relation, we will obtain the number of quantum states with energy less than ω. Then, it is used to calculate the statistical-mechanical entropy of the scalar field in the Schwarzschild black hole spacetime. By taking exact method, we obtained the leader term of entropy which is proportional to the event horizon area and correction terms take the forms of ln A, A ⁻¹ln A, A ⁻¹ and so on.     

Structure and melting of dipole clusters

Two-dimensional microclusters made up of particles repelled by the dipole law and confined by an external quadratic potential are considered. The model describes a number of physical systems, in particular, electrons in semiconductor structures near a metallic electrode, indirect excitons in coupled semiconductor dots etc. Two competing types of particle ordering in clusters have been revealed: formation of a triangular lattice and of a shell structure. Equilibrium configurations of clusters with N=1–40 particles are calculated. Temperature dependences of the structure, potential energy, and mean-square radial and angular displacements are studied. These characteristics are used to investigate cluster melting. Melting occurs in one or two stages, depending on N. Melting of a two-shell microcluster takes place in two stages: at low temperatures—from the frozen phase to a state with rotationally reoriented “crystalline” shells with respect to one another, followed by a transition involving breakdown of radial order. Melting in a cluster made up of a larger number of shells occurs in one stage. This is due to the fact that the potential barrier to intershell rotation is substantially lower than that to particle jumping from one shell to another for small N, and of the same order of magnitude for large N. A method is proposed for predicting the character of melting in shell clusters by comparing the potential barriers for shell rotation and intershell particle jumping. Fiz. Tverd. Tela (St. Petersburg) 40, 1379–1386 (July 1998)     

The origin of thermal hadron production

Multihadron production in high energy collisions, from e⁺e^- annihilation to heavy ion interactions, shows remarkable thermal behaviour, specified by a universal “Hagedorn” temperature. We argue that this hadronic radiation is formed by tunneling through the event horizon of colour confinement, i.e., that it is the QCD counterpart of Hawking-Unruh radiation from black holes. It is shown to be emitted at a universal temperature T_H ≃ (σ/2 π)^1/2, where σ denotes the string tension. Since the event horizon does not allow information transfer, the radiation is thermal “at birth”.     

Gluon radiation outside a finite cone

The medium-induced gluon radiation angular distributions of light quarks and heavy quarks outside a finite jet cone are studied. We find the effect of destructive interference between the vacuum and medium-induced radiation plays an important role in gluon radiation for very small value of path length L, which leads to the negative value of medium-induced energy loss. The medium-induced radiative energy loss outside an angle for heavy quarks is found to have a minimum and a maximum at small angle for small path length, which are caused by dead cone effect and Brownian k _⊥-broadening effect, respectively. However for large path length the minimum and maximum disappear.     

Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000     

Critical velocity and event horizon in pair-correlated systems with “relativistic” fermionic quasiparticles

The condition for the appearance of an event horizon is considered in pair-correlated systems (superfluids and superconductors) in which the fermionic quasiparticles obey “relativistic” equations. In these systems the Landau critical velocity of superflow corresponds to the speed of light. In conventional systems, such as s-wave superconductors, the superflow remains stable even above the Landau threshold. We show, however, that, in “ relativistic” systems, the quantum vacuum becomes unstable and the superflow collapses after the “speed of light” is reached, so that the horizon cannot appear. Thus an equilibrium dissipationless superflow state and the horizon are incompatible on account of quantum effects. This negative result is consistent with the quantum Hawking radiation from the horizon, which would lead to a dissipation of the flow. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 124–129 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Optimal investment horizons

In stochastic finance, one traditionally considers the return as a competitive measure of an asset, i.e., the profit generated by that asset after some fixed time span Δt, say one week or one year. This measures how well (or how bad) the asset performs over that given period of time. It has been established that the distribution of returns exhibits “fat tails” indicating that large returns occur more frequently than what is expected from standard Gaussian stochastic processes [1-3]. Instead of estimating this “fat tail” distribution of returns, we propose here an alternative approach, which is outlined by addressing the following question: What is the smallest time interval needed for an asset to cross a fixed return level of say 10%? For a particular asset, we refer to this time as the investment horizon and the corresponding distribution as the investment horizon distribution. This latter distribution complements that of returns and provides new and possibly crucial information for portfolio design and risk-management, as well as for pricing of more exotic options. By considering historical financial data, exemplified by the Dow Jones Industrial Average, we obtain a novel set of probability distributions for the investment horizons which can be used to estimate the optimal investment horizon for a stock or a future contract. Received 20 February 2002 Published online 25 June 2002     

Fermi surface of doped lithium

The Korringa-Kohn-Rostoker method with Green’s function averaged over the atomic configurations in a complex Ising lattice and a muffin-tin potential was used to calculate the electronic-band structure in lithium containing vacancies and s, p, and d impurities. It is shown that substantial changes in the profile of the Fermi surface do not lead to necking, as was postulated previously, but cause splitting of the electronic states at the face of the Brillouin zone. This is attributed to the reduced symmetry of the crystal lattice with impurity excitation of the electronic-subsystem. Fiz. Tverd. Tela (St. Petersburg) 40, 1185–1186 (July 1998)     

Bohr-Coster diagrams for multiply ionized states of light elements in the rangeZ = 10 to 20

Calculations in the L-S coupling approximation of the average total energies of various defect electron configurations with single or doubleK shell and varying number ofL shell vacancies for some light elements in the rangeZ = 10 to 20 are reported. The calculations show that the linear trend observed for normal Bohr-Coster diagrams (√E vsZ curves for the usual X-ray energy states) persists in the case of multiply ionized atomic states as well.     

Interactions of like-charged rods at low temperatures: Analytical theory vs. simulations

We investigate a system consisting of two like-charged infinitely long rods and neutralizing counterions at low temperatures, using both analytic theory and simulations. With some reasonable approximations we can analytically solve for several ground-state structures of the model, starting with states where all counterions are lined up in the gap between the rods, over planar configurations, where the counterions are divided up into a fraction which resides between the rods, and counterions which are located on the outer surfaces, up to configurations which cover the full rod surfaces. Using parallel tempering simulations, we are able to study the system over a wide range of temperatures. At low temperatures we find good agreement with our T = 0 results. At higher temperatures, the strong coupling (SC) theory delivers qualitatively better results. We furthermore demonstrate that for the SC theory and our ground-state approximations to yield quantitative agreement, three parameters are required to be large, the strong-coupling parameter Ξ, the Rouzina-Bloomfield parameter, and the ratio of the average distance of the counterions to the radius of the rods. In the case of the latter ratio being small, our T = 0 results show better agreement with the simulation data at very low temperatures.     

Level density and shape changes in excited sd shell nuclei

In the present calculation we have used the Monte Carlo method of generating collective spin and total energy of the nucleus for various configurations of the system with N ₀ single particle states available for n number of particles. The different configurations (arrangements of occupied single particle states) leading to a particular energy E and spin J are then collected to get the density of states for the given energy E and spin J. We find that if we use the cranked Nilsson model single particle states for the rotational frequency Ω = 0.0ħω, 0.05ħω and 0.1ħω there is a shift in the maximum density of states W _max with a tendency for the system to become more oblate or prolate depending on the shift in the maximum density of states as the angular momentum decreases or increases. The change in nuclear level density with collectivity, i.e. with the use of cranked Nilsson model single particle levels has been noticed.