The Hawking radiation of the charged particle via tunnelling from the axisymmetric Sen black hole

Extending Parikh's semi-classical quantum tunnelling model, this paper has studied the Hawking radiation of the charged particle via tunnelling from the horizon of the axisymmetric Sen black hole. Different from the uncharged massless particle, the geodesics of the charged massive particle tunnelling from the horizon is not light-like. The derived result supports Parikh's opinion and provides a correct modification to Hawking strictly thermal spectrum developed by the fixed background space-time and not considering the energy conservation and the self-gravitation interaction.     

Conduction bands in classical periodic potentials

The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time to perform the measurement. This paper considers the possibility that ΔE, the uncertainty in the energy, may be complex. To understand the effect of a particle having a complex energy, the behaviour of a classical particle in a one-dimensional periodic potential V(x) = −cos(x) is studied. On the basis of detailed numerical simulations it is shown that if the energy of such a particle is allowed to be complex, the classical motion of the particle can exhibit two qualitatively different behaviours: (i) The particle may hop from classically allowed site to nearest-neighbour classically allowed site in the potential, behaving as if it were a quantum particle in an energy gap and undergoing repeated tunnelling processes or (ii) the particle may behave as a quantum particle in a conduction band and drift at a constant average velocity through the potential as if it were undergoing resonant tunnelling. The classical conduction bands for this potential are determined numerically with high precision.     

The symmetry group paradox for non-rigid molecules

In many situations, the energy levels for a quantum system, whose Hamiltonian is invariant under a specific symmetry group, are split when the Hamiltonian is replaced by a new one with lower symmetry. In non-rigid molecules (NRM), fast quantum tunnelling processes allow the molecule to change between different geometrical configurations related by permutations of identical nuclei (or with inversion as well), resulting in the splitting of the energy levels for the rigid molecule (RM) case where tunnelling is absent. However, for NRM, there is apparently a paradoxical situation where although the original RM energy levels are associated with a symmetry group isomorphic to the point group for the geometrical configuration, the split NRM energy levels are associated with a symmetry group consisting of all permutations and inversions related to the fast quantum tunnelling processes between configurations, and for which the point group is a subgroup. The resolution of this paradox, where energy level splitting is evidently accompanied by an enlargement of the symmetry group, is the subject of this article.     

Dirac operator on the sphere with attached wires

An explicitly solvable model for tunnelling of relativistic spinless particles through a sphere is suggested. The model operator is constructed by an operator extensions theory method from the orthogonal sum of the Dirac operators on a semiaxis and on the sphere. The transmission coefficient is obtained. The dependence of the transmission coefficient on the particle energy has a resonant character. One observes pairs of the Breit–Wigner and the Fano resonances. It correlates with the corresponding results for a non-relativistic particle.     

The quantum tunnelling radiation of Schwarzschild de Sitter black hole with a global monopole

Applying Parikh's quantum tunnelling method, this paper has studied the quantum tunnelling radiation of Schwarzschild de Sitter black hole with a global monopole. The result shows that the tunnelling rates at the event horizon and the cosmological horizon are related to Bekenstein--Hawking entropy and the derived radiation spectrum is not precisely thermal when considering energy conservation and self-gravitation interaction.     

Understanding the reaction between muonium atoms and hydrogen molecules: zero point energy,tunnelling, and vibrational adiabaticity

The advent of very precise measurements of rate coefficients in reactions of muonium (Mu), the lightest hydrogen isotope, with H₂ in its ground and first vibrational state and of kinetic isotope effects with respect to heavier isotopes has triggered a renewed interests in the field of muonic chemistry. The aim of the present article is to review the most recent results about the dynamics and mechanism of the reaction Mu+H₂ to shed light on the importance of quantum effects such as tunnelling, the preservation of the zero point energy, and the vibrational adiabaticity. In addition to accurate quantum mechanical (QM) calculations, quasiclassical trajectories (QCT) have been run in order to check the reliability of this method for this isotopic variant. It has been found that the reaction with H₂(v=0) is dominated by the high zero point energy (ZPE) of the products and that tunnelling is largely irrelevant. Accordingly, both QCT calculations that preserve the products’ ZPE as well as those based on the Ring Polymer Molecular Dynamics methodology can reproduce the QM rate coefficients. However, when the hydrogen molecule is vibrationally excited, QCT calculations fail completely in the prediction of the huge vibrational enhancement of the reactivity. This failure is attributed to tunnelling, which plays a decisive role breaking the vibrational adiabaticity when v=1. By means of the analysis of the results, it can be concluded that the tunnelling takes place through the ν₁=1 collinear barrier. Somehow, the tunnelling that is missing in the Mu+H₂(v=0) reaction is found in Mu+H₂(v=1).     

Classical and quantum magnetisation reversal studied in single nanometer-sized particles and clusters using micro-SQUIDs

Recent progress in experiment on quantum tunnelling of the magnetic moment in mesoscopic systems will be reviewed. The emphasis will be made on measurements of individual nanoparticles. These nanomagnets allow one to test the border between classical and quantum behaviour. Using the micro-SQUID magnetometer, waiting time, switching field and telegraph noise measurements show unambiguously that the magnetisation reversal of small enough single-crystalline nanoparticles is described by a model of thermal activation over a single-energy barrier. Results on insulating BaFeO nanoparticles show strong deviations from this model below 0.4 K which agree with the theory of macroscopic quantum tunnelling in the low dissipation regime.     

非线性朗道-基纳隧穿

介绍一种新的量子隧穿———非线性朗道-基纳隧穿.这种隧穿一般发生在有相互作用的二能级系统中,比如光晶格中的玻色-爱因斯坦凝聚物和分子磁体.相对于传统的线性朗道-基纳隧穿,非线性朗道-基纳隧穿由排斥相互作用带来的非线性会增强隧穿的概率.特别是当非线性非常强时,系统的绝热性会遭到破坏;一个无穷小的线性驱动都会造成有限的隧穿概率.     

Hartman effect in presence of Aharanov-Bohm flux

The Hartman effect for a tunnelling particle implies the independence of group delay time on the opaque barrier width with superluminal velocities as a consequence. This effect is further examined on a quantum ring geometry in the presence of Aharonov-Bohm flux. We show that while tunnelling through an opaque barrier, the group delay time for given incident energy becomes independent of the barrier thickness as well as the magnitude of the flux. The Hartman effect is thereby extended beyond one dimension in the presence of Aharonov-Bohm flux.     

Dephasing of quantum tunnelling in molecular nanomagnets

Dephasing mechanism of quantum tunnelling in molecular magnets has been studied by means of the spin-coherentstate path integral in a mean field approximation. It is found that the fluctuating uncompensated transverse field from the dipolar-dipolar interaction between molecular magnets contributes a random phase to the quantum interference phase. The resulting transition rate is determined by the average tunnel splitting over the random phase. Such a dephasing process leads to the suppression of quenching due to the quantum phase interference, and to the steps due to odd resonances in hysteresis loop survived, which is in good agreement with experimental observations in molecular nanomagnets Fes and Mn12.     

Massive particles＇ tunnelling radiation from the black hole with a mass-quadruple moment

In this paper, we extend Zhang and Zhao's recent work to the black hole with a mass-quadruple moment. The behaviour of the tunnelling massive particles is investigated, and the emission rate at which massive particles tunnel across the event horizon of the black hole is calculated. The result is consistent with an underlying unitary theory, and takes the same functional form as that of a massless particle.     

Optimised polychromatic field-mediated suppression of H-atom tunnelling in a coupled symmetric double well: two-dimensional malonaldehyde model

The cis–cis isomerisation motion of malonaldehyde can be modelled as a symmetric double well coupled with an asymmetric double well, which includes the effect of the cis–trans out-of-plane motion on the cis–cis motion. We have presented an effective method for having control over the tunnelling dynamics of the symmetric double well which is coupled with the asymmetric double well by monitoring tunnelling splitting. When a suitable external field is allowed to interact with the system, the tunnelling splitting gets modified. As the external time perturbation is periodic in nature, the Floquet theory can be applied to calculate the quasi-energies of the perturbed system and hence the tunnelling splitting. The Floquet analysis is coupled with a stochastic optimiser in order to minimise the tunnelling splitting, which is related to slowering of the tunnelling process. The minimisation has been done by one of the stochastic optimisers, simulated annealing. Optimisation has been performed on the parameters which define the external polychromatic field, such as intensities and frequencies of the components of the polychromatic field. With the optimised sets of parameters, we have followed the dynamics of the system and have found suppression of tunnelling which is manifested by a much higher tunnelling time.     

Fermions’ Tunnelling from the Reissner- Nordström-Anti-de Sitter Black Hole

Very recent work of Kerner and Mann involving fermions tunnelling from the Rindler space-time and a general non-rotating black hole is extended to the case of Reissner-Nordström-anti-de Sitter black hole. Due to the couple between the gravity field and electromagnetic field, we introduce the Dirac equation of the charged particles to determine the action of the radiation. We further consider the correction of the thermal spectrum in the unfixed background space time. It is shown that when the energy and charge conservations are considered, the tunnelling rate of fermions is also related to the change of Bekenstein-Hawking entropy, implying the underlying unitary theory is satisfied.     

Investigation of gate current in nano-scale MOSFETs by Monte Carlo solution of quantum Boltzmann equation

This paper investigates gate current through ultra-thin gate oxide of nano-scale metal oxide semiconductor field effect transistors (MOSFETs), using two-dimensional (2D) full-band self-consistent ensemble Monte Carlo method based on solving quantum Boltzmann equation. Direct tunnelling, Fowler--Nordheim tunnelling and thermionic emission currents have been taken into account for the calculation of total gate current. The 2D effect on the gate current is investigated by including the details of the energy distribution for electron tunnelling through the barrier. In order to investigate the properties of nano scale MOSFETs, it is necessary to simulate gate tunnelling current in 2D including non-equilibrium transport.     

On the role of quantum tunnelling and statistical effects in the liquid gas phase transition of hot nuclei

The triggering of the liquid-gas phase transition in hot nuclear matter by quantum and statistical fluctuations is studied in a microscopic approach to nucleation which is a fluid-dynamical version of the imaginary-time dependent mean-field theory at finite temperature. It is found that quantum tunnelling processes are only important below T = 1 MeV.     

Tunnelling effect from a Vaidya--de Sitter black hole

In this paper, we extend Parikh' recent work to the Vaidya--de Sitter black hole which is non-stationary. We view Hawking radiation as a tunnelling process across the event horizon and calculate the tunnelling probability when the particle crosses the event horizon. From the tunnelling probability we also find a leading correction to the semiclassical emission rate.     

Atomic Tunnelling Dynamics of Two Squeezed Bose-Einstein Condensates

In this paper, tunnelling dynamics of squeezed Bose-Einstein condensates (BEC's) in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunnelling interaction is investigated by using the second quantization approach. The influence of BEC squeezing on macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunnelling is analyzed in detail. It is shown that the MQST and coherent atomic tunnelling between two squeezed BEC's can be manipulated through changing squeezing amplitude and squeezing phase of BEC squeezed states.     

Quantum diffusion of a particle in a periodic potential with ohmic dissipation

The motion of a particle in a periodic potential is studied at low temperatures where transitions between the potential wells are caused by quantum tunnelling. The theory accounts for the dissipative interaction with an environment which for a wide range of parameters leads to incoherent tunnelling at a rate with a nonanalytic temperature dependence. The influence of an external force is determined and a nonanalytic response is found at T = 0. The case of a biased double-well system is treated too.     

(CdZnTe,ZnS)/ZnTe复合量子阱的光学特性研究

设计并制备了一种新型的(CdZnTe,ZnS)/ZnTe复合量子阱结构.使CdZnTe量子阱中的激子有可能在短时间内隧穿到ZnS阱层,从而达到提高光双稳器件“关”速度的目的.并通过对发光特性的研究证实在我们设计的结构中横向激子隧穿的存在,从而为进一步研究超高速光开关提供了实验依据.