Fermi Acceleration in driven relativistic billiards

We show numerical experiments of driven billiards using special relativity. We have the remarkable fact that for the relativistic driven circular and annular concentric billiards, depending on initial conditions and parameters, we observe Fermi Acceleration, absent in the Newtonian case. The velocity for these cases tends to the speed of light very quickly. We find that for the annular eccentric billiard the initial velocity grows for a much longer time than the concentric annular billiard until it asymptotically reach c.     

Fermi Acceleration in Anti-Integrable Limits of the Standard Map

We consider a dynamical system on the semi-infinite cylinder which models the high energy dynamics of a family of mechanical models. We provide conditions under which we ensure that the set of orbits undergoing Fermi acceleration has measure zero.     

Quantized Fermi Accelerator: A Soluble Model for Quantum Friction

The motion of a particle constrained to move inside a box with a movable wall is quantized. The semiclassical, adiabatic and exact solutions are worked out. The time-dependent density matrix is found in closed form. The motions of the heavy and the light parts of the system, described by appropriate reduced density matrices, are discussed. General comments about quantum friction are made.     

A Theory for Quantum Accelerator Modes in Atom Optics

Unexpected accelerator modes were recently observed experimentally for cold cesium atoms when driven in the presence of gravity. A detailed theoretical explanation of this quantum effect is presented here. The theory makes use of invariance properties of the system, that are similar to the ones of solids, leading to a separation into independent kicked rotor problems. The analytical solution makes use of an asymptotic approximation very similar to the semiclassical one, except that the small parameter is not Planck's constant, but rather the detuning from the frequency that is resonant in absence of gravity.     

First and Second Sound Modes in a Uniform Fermi Gas

First and second sound modes in a uniform fermionic atom gas with Feshbaeh resonance are investigated in the frame of a two-fluid model at finite temperature. All thermodynamic quantities axe calculated for a given thermodynamic potential. The analytical results for thermodynamic quantities and sound velocities in BCS and BEC limits are obtained. The numerical results show that there exists a continuous interpolation for sound velocities of the first and second sound modes at fixed T/Tc between BCS and BEC limits. The existence of the second sound mode indicates the existence of superfluidity.     

Collective Modes of a Quasi-Two-Dimensional Superfluid Fermi Gas in BCS-BEC Crossover

We investigate the collective modes of a quasi-two-dimensional （Q2D） superfluid Fermi gas in Bardeen-Cooper-Schrieffer Bose-Einstein condensation （BCS-BEC） crossover. For solving a generalized Gross-Pitaevskii equation by using a time-dependent variational method, we take a trial wavefunction with the form of hybrid Gaussianparabolic type, which not only reflects the Q2D character of the system and also allows an essentially analytical approach of the problem. We present a Q2D criterion that is valid for various superfluid regimes and displays clearly the relation between the maximum condensed particle number and the parameters of trapping potential as well as atom-atom interaction. We show that due to the small particle number in the Q2D condensate, the contribution to oscillating frequencies by the quantum pressure in the strong confinement direction is significant and hence a Thomas-Fermi approximation can not be used.     

Dynamical Properties of the Unitary Fermi Gas: Collective Modes and Shock Waves

We discuss the unitary Fermi gas made of dilute and ultracold atoms with an infinite s-wave inter-atomic scattering length. First we introduce an efficient Thomas–Fermi–von Weizsacker density functional which describes accurately various static properties of the unitary Fermi gas trapped by an external potential. Then, the sound velocity and the collective frequencies of oscillations in a harmonic trap are derived from extended superfluid hydrodynamic equations which are the Euler–Lagrange equations of a Thomas–Fermi–von Weizsacker action functional. Finally, we show that this amazing Fermi gas supports supersonic and subsonic shock waves.     

Accelerator development in India

Accelerator development in India is reviewed with special emphasis on indigenous effort. It started with the 4 MeV cyclotron at the Saha Institute of Nuclear Physics, grew substantially with the installation of the Van de Graaff accelerators at Trombay and really came of age with the 224 cm Variable Energy Cyclotron at Calcutta, which resulted in considerable fall-out of technology. Simultaneously electron linac development has also taken place. Thus the stage is set for developing new types of accelerators such as the electron storage ring synchroton, and a proton/heavy ion synchrotron.     

Enrico Fermi in Pisa

I discuss the early work of Enrico Fermi (1901-1954) as a student in Pisa at the Scuola Normale Superiore and at the University of Pisa (1918-1922), paying particular attention to the four papers he published during those years and to his licenza and doctoral theses.     

Instabilities of a Fermi Gas with Nested Fermi Surfaces

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a vector Q commensurate with the lattice in conjunction with the interaction between the quasiparticles can give rise to a rich phase diagram. Of particular importance is itinerant antiferromagnetic order in the context of pnictides and heavy fermion compounds. By mismatching the nesting the order can gradually be suppressed and as the Néel temperature tends to zero a quantum critical point is obtained. A superconducting dome above the quantum critical point can be induced by the transfer of pairs of electrons between the pockets. The conditions under which such a dome arises are studied. In addition numerous other phases may arise, e.g. charge density waves, non‐Fermi liquid behavior, non‐s‐wave superconductivity, Pomeranchuk instabilities of the Fermi surface, nematic order, and phases with persistent orbital currents.     

Accelerator neutrino beams

Neutrino beams at from high-energy proton accelerators have been instrumental discovery tools in particle physics. Neutrino beams are derived from the decays of charged π$\pi$ and K   mesons, which in turn are created from proton beams striking thick nuclear targets. The precise selection and manipulation of the π/K$\pi /K$ beam control the energy spectrum and type of neutrino beam. This article describes the physics of particle production in a target and manipulation of the particles to derive a neutrino beam, as well as numerous innovations achieved at past experimental facilities.     

Metastability in spin-polarized Fermi gases

We study the role of particle transport and evaporation on the phase separation of an ultracold, spin-polarized atomic Fermi gas. We show that the previously observed deformation of the superfluid paired core is a result of evaporative depolarization of the superfluid due to a combination of enhanced evaporation at the center of the trap and the inhibition of spin transport at the normal-superfluid phase boundary. These factors contribute to a nonequilibrium jump in the chemical potentials at the phase boundary. Once formed, the deformed state is highly metastable, persisting for times of up to 2?s.     

Fermi surface reconstruction in strongly correlated Fermi systems as a first-order phase transition

A quantum phase transition in strongly correlated Fermi systems beyond the topological quantum critical point has been studied using the Fermi liquid approach. The transition takes place between topologically equivalent states with three Fermi surface sheets, but one of them is characterized by a quasiparticle halo in the quasiparticle momentum distribution n(p), and the other one is characterized by a hole pocket. It has been found that the transition between these states is a first-order phase transition for the interaction constant g and temperature T. The phase diagram in the vicinity of this transition has been constructed.     

Pendulum in a Fermi liquid

The Fermi-liquid theory formulated by Landau is a basic paradigm of the behavior of an interacting many-body system. We present a new application of this theory to calculate the "Landau force" on a macroscopic object. We show that immersing a pendulum in a Fermi liquid can increase its oscillation frequency, and evidence of this has been observed in mixtures of (3)He and (4)He.     

Fermi Gas in D-Dimensional Space

We consider a Fermi gas in D-dimensional spaceand show how the physical properties of the systembehave as a function of the dimension D, in particular,the density of states, the Fermi energy, and the radius of the Fermi hypersphere.     

Fermi motion in hypernuclear production

The effects of target-nucleon motion in the (K, π) reaction are studied. The distortion of meson waves and the full transition amplitude are taken into account. The renormalization of the A-body transition matrix due to Fermi motion does not reduce theoretical cross sections substantially.     

Weyl transformation in Fermi systems

In the path integral representation, the Hamiltonian in a quantum system is associated with the Hamiltonian in a classical system through the Weyl transformation. From this, it is possible to describe the time evolution in a quantum system by the Hamiltonian in a classical system. In a Bose system, the Weyl transformation is defined by the eigenstates of the canonical operators, since the Hamiltonian is given by a function of the canonical operators. On the other hand, in a Fermi system, the Hamiltonian is usually described by a function of the creation and annihilation operators, and hence the Weyl transformation is defined by the coherent states which are the eigenstate of an annihilation operator. Here, we formulate the Weyl transformation in Fermi systems in terms of the eigenstates of the canonical operators so as to clarify the correspondence between both systems. Using this, we can derive the path integral representation in Fermi systems.     

Collective coordinates in Fermi systems

The problem of developing a consistent perturbation theory for a Fermi system in the case in which the unperturbed system exhibits dynamical symmetry breaking is discussed, by using collective coordinate methods. By adapting to this problem the methods used in the quantization of gauge theories, it is shown how to deal with composite zero-frequency excitations in such a way that the resulting perturbation theory is free of infrared divergencies. Explicit calculations are carried out in the case of a simple quantum mechanical model representing a superfluid Fermi system.     

A TB-Mode Accelerator

An accelerator is proposed in which a TE-mode wave is used to drive charged particles in contrast to the usual linear accelerators in which longitudinal electric fields or TM-mode waves are supposed to be utilized. The principle of the acceleration is based on the Vp × B acceleration of a dynamo force acceleration. That is, a charged particle trapped in a transverse wave feels a constant electric field (Faraday induction field) and subsequently is accelerated when an appropriate magnetic field is externally applied in the direction perpendicular to the wave propagation. A pair of dielectric plates is used to produce a slow TE mode. Discussions will be given on what the conditions of the particle trapping are and how to stabilize the particle orbit.     

Fermi surface effect on intrinsic Lorenz number of Fermi liquids

We investigate a Fermi surface effect on the ideal Lorenz ratio of an anisotropic Fermi liquid caused by the onset of Umklapp scatterings. After discussing simple models by way of illustration, we present numerical results for transition metals, and indicate a material with a simple Fermi surface like sodium cobaltite as a possible candidate to observe the effect.