Quantum Degeneracy Research Articles

Global weak solution to the degenerate quantum Navier‐Stokes‐Maxwell equations with damping term

AbstractIn this paper we investigate the global existence of the finite energy weak solution to the isentropic quantum Navier‐Stokes‐Maxwell equations with density‐dependent viscosity and the damping term in three‐dimensional periodic domain. This model is composed of the isentropic compressible Navier‐Stokes‐Maxwell equation with density‐dependent viscosity, the quantum Bohm potential and a damping term. This model can be used to describe the motion of the particle in the plasma under the electric–magnetic field. The main techniques are the Faedo‐Galerkin method, some imbedding inequalities and some compactness theorems.

Quantum mechanism of extremely high energy processes at neutron star collapse and of quasar luminosity

Using the braid group topological approach to quantum statistics we demonstrate that for strong gravitational field occurring in neutron star merger with mass exceeding the Tolman, Oppenheimer and Volkoff limit the quantum statistics of particles beneath the photon sphere decays, which results in an instant relief of quantum degeneracy pressure in the star. This causes a rapid shrink of the matter to a black hole with quite different quantum collective character of particles. The scheme of neutron Fermi sphere collapse is proposed as the possible isotropic source of short giant gamma-ray bursts. The similar quantum mechanism of collapse of Fermi spheres of electrons and protons in plasma of accretion disc in vicinity of the Schwarzschild horizon of galactic black hole is able to elucidate the giant luminosity of remote quasars. The efficiency of the mass to energy conversion via collapse of the Fermi sphere is ca. 30 %, not reachable for any other known physical process except of the matter-antimatter annihilation.

Achieving ultracold Bose–Fermi mixture of 87Rb and 40K with dual dark magnetic-optical-trap

We demonstrate that dual dark magnetic-optical-traps (MOTs) have great importance in the two-species 87Rb and 40K mixture compared with dual bright MOTs. The dark MOT has a little improvement in the trapping of single-species 87Rb or 40K gases compared with bright MOT. For the case of loading two-species 87Rb and 40K simultaneously, the improvement of 40K in the dual dark MOTs is mainly from the reduction of light-assisted collision losses. The dual dark MOTs employ a pair of conical lenses to produce the hollow beam for repump laser with high efficiency. The number and density of 87Rb and 40K atoms after evaporative cooling in the hybrid magnetic trap with dark MOT loading are compared with those in bright MOT. The atoms with large number and high density make it easier to realize the quantum degenerate of Bose–Fermi mixture.

Quantum Mechanical Meaning of the Charge Transfer Resistance

In a previous work on the quantum rate interpretation of the electron transfer occurring in heterogeneous electrochemical interfaces, we demonstrated that a quantum mechanical rate principle can be used to calculate the electron transfer rate constant of diffusionless electrochemical reactions. This calculation was demonstrated to be possible by simply taking a single specific value of a current–voltage electrochemical curve from which the quantum capacitance of the electrochemical interface is obtained. The method is supported by the fact that the quantum of conductance is related to the quantum capacitance and the ratio between these quantities defines the quantum rate of the electrochemical reaction whenever the quantum degeneracy is rightly defined. In the present work, we applied capacitance-derived electrochemical impedance spectroscopy not only to confirm our conclusions stated in previous works but also to establish the quantum mechanical meaning of the charge transfer resistance which, as will be demonstrated, is correlated to the transmission coefficient within the quantum rate theory. Accordingly, we experimentally demonstrated that the resistance to the transfer of a single charge at the interface occurred with a value of ∼13.0 ± 0.4 kΩ that conformed with the nanoscale electronic interpretation of the quantum of resistance, theoretically expected to be ∼12.9 kΩ. The value of ∼13 kΩ, as a physical and quantized resistive limit, not only agrees with the theory but also cannot be interpreted in isolation, requiring a consideration of resistances of contact and electrolyte contained in the definition of charge transfer resistance. Our findings confirm that electrochemistry and nanoscale electronics, within a suitable quantum mechanical interpretation of the electron dynamics, have a common foundation in quantum mechanics. This work indicates that controlling the properties of electrochemical interfaces at the nanometer molecular scale will enable the development of novel and advanced electrochemical quantum devices.

Vortex counting and the quantum Hall effect

We provide evidence for conjectural dualities between nonrelativistic Chern-Simons-matter theories and theories of (fractional, nonAbelian) quantum Hall fluids in 2 + 1 dimensions. At low temperatures, the dynamics of nonrelativistic Chern-Simons-matter theories can be described in terms of a nonrelativistic quantum mechanics of vortices. At critical coupling, this may be solved by geometric quantisation of the vortex moduli space. Using localisation techniques, we compute the Euler characteristic χ( mathcal{L} λ) of an arbitrary power λ of a quantum line bundle mathcal{L} on the moduli space of vortices in U(Nc) gauge theory with Nf fundamental scalar flavours on an arbitrary closed Riemann surface. We conjecture that this is equal to the dimension of the Hilbert space of vortex states when the area of the metric on the spatial surface is sufficiently large. We find that the vortices in theories with Nc = Nf = λ behave as fermions in the lowest nonAbelian Landau level, with strikingly simple quantum degeneracy. More generally, we find evidence that the quantum vortices may be regarded as composite objects, made of dual anyons. We comment on potential links between the dualities and three-dimensional mirror symmetry. We also compute the expected degeneracy of local Abelian vortices on the Ω-deformed sphere, finding it to be a q-analog of the undeformed case.

Overtaking Interactions of Multi-Ion Acoustic Shock Waves in a Magnetized Degenerate Plasma: An Application in White Dwarfs

Overtaking interactions are examined of multi-ion acoustic shock waves in magnetized degenerate quantum plasmas comprising inertial non-relativistic heavy and light ions having positive charges ultra-relativistic degenerate inertialess electrons. A Burgers’ equation governs the nonlinear excitation of multi-ion acoustic shock waves in a plasma model at hand. The Cole-Hopf transformation and the exponential function have been used to study the overtaking interactions of multi-ion acoustic shock waves in two modes (i.e., the fast and the slow modes). Numerically, the compressive ion-acoustic shock waves exist for the fast mode, but the rarefactive ion-acoustic shock waves exist for the slow mode. A numerical simulation demonstrates that the overtaking interactions of multi-ion acoustic shock waves and their electric fields are remarkably modified with the effectiveness of the charge states of heavy ions and light ions. Furthermore, the amplitude and the steepness of multi-ion acoustic shock waves increase with the decrease in the directional cosines of the multi-ion acoustic shock waves vector along the z-axis. Numerical simulations of overtaking interaction are employed to significantly highlight the physical features of multi-ion acoustic shock waves in astrophysical situations such as white dwarfs and neutron stars.

Arbitrary-amplitude self-gravitational solitary potential in a degenerate quantum plasma system

Arbitrary-amplitude self-gravitational solitary potential in a degenerate quantum plasma system

Extracting non-Abelian quantum metric tensor and its related Chern numbers

The complete geometry of quantum states in parameter space is characterized by the quantum geometric tensor, which contains the quantum metric and Berry curvature as the real and imaginary parts, respectively. When the quantum states are degenerate, the quantum metric and Berry curvature take non-Abelian forms. The non-Abelian (Abelian) Berry curvature and Abelian quantum metric have been experimentally measured. However, an experimentally feasible scheme to extract all the components of the non-Abelian quantum metric tensor is still lacking. Here we propose a generic protocol to directly extract the non-Abelian quantum metric tensor in arbitrary degenerate quantum states in any dimensional parameter space, based on measuring the transition probabilities after parameter quenches. Furthermore, we show that the non-Abelian quantum metric can be measured to obtain the real Chern number of a generalized Dirac monopole and the second Chern number of a Yang monopole, which can be simulated in three and five-dimensional parameter space of artificial quantum systems, respectively. We also demonstrate the feasibility of our quench scheme for these two applications with numerical simulations.

The methods of thermal field theory for degenerate quantum plasmas in astrophysical compact objects

In the study of degenerate plasmas contained within compact astrophysical objects, both special relativity and general relativity play important roles. After reviewing the existing treatment in the literature, here we employ the methods of relativistic thermal quantum field theory to compute the equation of states of degenerate matter for compact astrophysical objects such as the white dwarfs and the neutron stars. In particular, we compute the equation of states that include leading order corrections due to the finite temperature, the fine-structure constant as well as the effect of gravitational time dilation. We show that the fine-structure constant correction remains well-defined even in the non-relativistic regime in contrast to the existing treatment in the literature.

Impact of Chen-Ning Yang’s theoretical work on ultracold atomic physics

As early as the 1950s, Prof. Yang and his collaborators realized that the most important interaction effects in a dilute quantum gas can be described by the s-wave scattering length between particles. This insight leads to universal descriptions of the interaction effects without the detailed knowledge of the interaction potential. They derived a formula expanding the energy density in terms of the gas parameter. This formula is later known as the Lee-Huang-Yang correction. However, it took forty years for the experimentalists to overcome several challenges and finally achieve degenerate quantum gases of atoms in 1995. The developments after 1995 have led to an exciting field known as “quantum gases” or “ultracold atomic gases”. The ultracold atom system has flexible tunability, allowing both the scattering length and the dimensionality to vary. The Lee-Huang-Yang corrections were observed from several experiments on ultracold atoms by increasing the scattering length. In addition, by reducing the dimensionality to one-dimension, several experiments on ultracold atoms have confirmed the Yang-Yang thermodynamics for one-dimensional bosons that Prof. Yang obtained in the 1960s and the large-<i>N</i> limit of one-dimensional fermions that Prof. Yang obtained around 2010. By increasing the dimensionality through using the idea of synthetic dimension, the experiment on ultracold atoms has also demonstrated the Yang monopole in the<i> SU</i>(2) non-abelian gauge field proposed by Prof. Yang in the 1970s. All of these experiments show the long-lasting impact of Prof. Yang’s theoretical work over several decades.

Transport spectroscopy in degenerate quantum dot

Using the microscopic model proposed by us earlier, the tunnel current and differential conductivity through a degenerate quantum dot weakly coupled to the external electrodes, depending on the bias and gate voltages, were calculated. The behavior of this system is analyzed at two types of electron-electron interaction in the quantum dot: repulsive and attractive. It is shown that in the case of the attractive interaction, the dependence of electron levels occupation on voltage becomes nonlinear, and the transport properties of the system change dramatically. The method of transport spectroscopy made it possible to determine through which of the levels (both ground and excited) tunneling takes place depending on the applied voltages and to estimate the current through these levels, as well as the orientation of electron spins on them. The results can be used to understand and predict the properties of a quantum dot as a potential element for new generations of nanodevices and quantum computers.

Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising-Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids.

The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin- Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate.

Electromagnetically induced transparency under phase modulation of interacting radiations

We report the results of an analytical and numerical analysis of the evolution of nanosecond probe pulses in the case of electromagnetically induced transparency in the Λ-scheme of degenerate quantum transitions. It is assumed that the probe and control fields at the active medium input are elliptically polarised, and one of them is phase modulated. It is shown analytically that probe radiation in a medium is the sum of two normal modes propagating independently of each other. Because the group velocities of normal mode pulses are different, a single probe pulse entering the medium decays inside the medium into separate pulses, each of which transfers the energy of one of the normal modes. Numerical simulations have shown that with a sufficiently large phase modulation, normal modes, whose intensity on the input surface is described by a bell-shaped curve, turn into trains of subpulses in the medium. Phase modulation of the input field has practically no effect on the group propagation velocities of normal modes, but it reduces the transparency of the medium for probe radiation.

Thermodynamic characteristics of ideal quantum gases in harmonic potentials within exact and semiclassical approaches

We theoretically examine equilibrium properties of the harmonically trapped ideal Bose and Fermi gases in the quantum degeneracy regime. We analyze thermodynamic characteristics of gases with a finite number of atoms by means of the known semiclassical approach and perform comparison with exact numerical results. For a Fermi gas, we demonstrate deviations in the Fermi energy values originating from a discrete level structure and show that these are observable only for a small number of particles. For a Bose gas, we observe characteristic softening of phase transition features, which contrasts to the semiclassical predictions and related approximations. We provide a more accurate methodology of determining corrections to the critical temperature due to finite number of particles.

Laser cooling for quantum gases

Laser cooling exploits the physics of light scattering to cool atomic and molecular gases to close to absolute zero. It is the crucial initial step for essentially all atomic gas experiments in which Bose-Einstein condensation and, more generally, quantum degeneracy is reached. The ongoing development of laser-cooling methods has allowed more elements to be brought to quantum degeneracy, with each additional atomic species offering its own experimental opportunities. Improved methods are opening new avenues, for example, reaching Bose-Einstein condensation purely through laser cooling as well as the realization of continuous Bose-Einstein condensation. Here we review these recent innovations in laser cooling and provide an outlook on methods that may enable new ways of creating quantum gases.

Insights into Magnetic Properties of a Mixed Spin-Electron Model on Decorated Planar Lattices Composed of Half-filled Trigonal Bipyramids

A mixed spin-electron model on decorated planar lattices formed by corner-sharing trigonal bipyramids is exactly solved by imposing three mobile electrons per triangular cluster of each bipyramid by means of a generalized decoration-iteration mapping transformation. It is shown that the ground state of the model involves two spontaneously long-range ordered phases, namely, the classical phase with a perfect ferromagnetic arrangement of all particles and the macroscopically degenerate quantum one. The macroscopic degeneracy of the quantum phase lies in chiral degrees of freedom of the mobile electrons. Finite-temperature phase diagrams as well as temperature variations of the spontaneous magnetization, entropy, and specific heat clearly prove that the classical spin-electron arrangement is thermally almost twice more stable than the quantum one for some combinations of the model's parameters.

Landau damping of electron-acoustic waves due to multi-plasmon resonances

The linear and nonlinear theories of electron-acoustic waves (EAWs) are studied in a partially degenerate quantum plasma with two-temperature electrons and stationary ions. The initial equilibrium of electrons is assumed to be given by the Fermi–Dirac distribution at finite temperature. By employing the multi-scale asymptotic expansion technique to the one-dimensional Wigner–Moyal and Poisson equations, it is shown that the effects of multi-plasmon resonances lead to a modified complex Korteweg–de Vries (KdV) equation with a new nonlocal nonlinearity. In addition to giving rise to a nonlocal nonlinear term, the wave–particle resonance also modifies the local nonlinear coupling coefficient of the KdV equation. The latter is shown to conserve the number of particles; however, the wave energy decays with time. A careful analysis shows that the two-plasmon resonance is the dominant mechanism for nonlinear Landau damping of EAWs. An approximate soliton solution of the KdV equation is also obtained, and it is shown that the nonlinear Landau damping causes the wave amplitude to decay slowly with time compared to the classical theory.

Emergence of orbital two-channel Kondo effect in epitaxial TiN thin films

The continual scaledown and stringent defect control in electronic devices are opening up frontiers in Kondo effect-a powerful testbed for probing magnetic impurity coupling to a continuum of electronic states. In disordered ferromagnets, degenerate quantum states like two-level systems (TLS) with a pseudo-half spin can couple with the continuum to mimic Kondo physics, creating the orbital two-channel Kondo (2CK) effect below the characteristic Kondo temperature (TK). By employing vacuum-annealing to inject ∼12 at.% nitrogen vacancies (VN) in TiN1-x films, we generated room-temperature ferromagnetic ordering with 13.6 emu g−1 saturation magnetization. The transport characteristics exhibited non-Fermi-liquid (NFL) behavior below TK of 20.2 K. The orbital 2CK effect is signified by a clear transition from logarithmic (T < T0∼40 K), to square-root dependence (T < TK) and subsequent deviation from it (T < TD∼10 K) in resistivity upturn behavior in three distinct low-temperature regimes. By controlling VN, we establish the necessity of ferromagnetism and ultrafast tunneling centers for generating orbital 2CK effect and NFL behavior in disordered metallic systems, extending their scope in non-magnetic nanomaterials.

Simulations of future particle accelerators: issues and mitigations

The ever increasing demands placed upon machine performance have resulted in the need for more comprehensive particle accelerator modeling. Computer simulations are key to the success of particle accelerators. Many aspects of particle accelerators rely on computer modeling at some point, sometimes requiring complex simulation tools and massively parallel supercomputing. Examples include the modeling of beams at extreme intensities and densities (toward the quantum degeneracy limit), and with ultra-fine control (down to the level of individual particles). In the future, adaptively tuned models might also be relied upon to provide beam measurements beyond the resolution of existing diagnostics. Much time and effort has been put into creating accelerator software tools, some of which are highly successful. However, there are also shortcomings such as the general inability of existing software to be easily modified to meet changing simulation needs. In this paper possible mitigating strategies are discussed for issues faced by the accelerator community as it endeavors to produce better and more comprehensive modeling tools. This includes lack of coordination between code developers, lack of standards to make codes portable and/or reusable, lack of documentation, among others.

Propagatory dynamics of nucleus-acoustic waves excited in gyrogravitating degenerate quantum plasmas electrostatically confined in curved geometry

A theoretic model to investigate the dynamics of the longitudinal nucleus-acoustic waves (NAWs) in gyrogravitating electrostatically confined degenerate quantum plasma (DQP) system in spherically symmetric geometry is constructed. The model setup consists of non-degenerate heavy nuclear species (HNS), lighter nuclear species (LNS), and quantum degenerate electronic species (DES). It specifically considers the influences of the Bohm potential, Coriolis rotation, viscoelasticity, and electrostatic confinement pressure (ECP, scaling quadratically in density). A standard normal spherical mode analysis gives a generalized dispersion relation (septic). It highlights the dependency of various atypical instability response on the equilibrium plasma parameters. A numerical illustrative platform portrays that the relative nuclear charge-to-mass coupling parameter (beta) acts as a destabilizing agency and the heavy-to-light nuclear charge density ratio (mu) acts as a stabilizing agency in both the non-relativistic (NR) and ultra-relativistic (UR) limits. Another interesting conjuncture is that the Coriolis rotation introduces a destabilizing influence on the system in both the limits. The progressive analysis presented herein has correlations and consistencies in the dynamic growth backdrop of various compact astro objects and their circumvent atmospheres, such as white dwarfs, neutron stars, etc.