The many-body problem with an energy-dependent confining potential

We consider systems of N bosons bound by two-body harmonic interactions, whose frequency depends on the total energy of the system. Such energy dependent confining interactions between the bosons yield remarkable properties of the many-body system. As the quantum numbers increase, the total energy cannot exceed a saturation energy, which is independent of the number of particles N. Moreover, the ground state energy increases with N. As a result, the density of states tends rapidly to infinity as N and/or the quantum numbers increase.     

Fast convergence of path integrals for many-body systems

We generalize a recently developed method for accelerated Monte Carlo calculation of path integrals to the physically relevant case of generic many-body systems. This is done by developing an analytic procedure for constructing a hierarchy of effective actions leading to improvements in convergence of N-fold discretized many-body path integral expressions from 1/N to 1/Np for generic p. In this Letter we present explicit solutions within this hierarchy up to level p=5. Using this we calculate the low lying energy levels of a two particle model with quartic interactions for several values of coupling and demonstrate agreement with analytical results governing the increase in efficiency of the new method. The applicability of the developed scheme is further extended to the calculation of energy expectation values through the construction of associated energy estimators exhibiting the same speedup in convergence.     

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases in their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their numerical evaluation in the general case of D-dimensional space-time as well as in integer dimensions D = D₀ for different values of dimensions including the most important practical cases D₀ = 2, 3, 4. Substantial simplifications occur for odd integer space-time dimensions where the final results can be expressed in closed form through elementary functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology where an irreducible loop is added.     

A nontrivial vacuum state in D = 10, N = 1 supergravity

We find a ground state of D = 10, N = 1 supergravity of the form (AdS(3) × R¹) × S³ × T³ which preserves all supersymmetries and should provide a gauged D = 4, N = 4 supergravity coupled to supermatter after dimensional reduction.     

237Np Mössbauer studies on actinide superconductors and related materials

Actinide materials play a special role in condensed matter physics, spanning behaviours of itinerant d-electron and localized 4f-electron materials. This duality of the 5f electrons confer to actinide-based intermetallic compounds a broad variety of physical properties such as magnetic or multipolar ordering, heavy fermion behaviour, quantum criticality, unconventional superconductivity... ²³⁷Np Mössbauer spectroscopy is a unique microscopic tool for gaining information on the electronic and magnetic properties of Np systems.     

Boson-like quantum dynamics of association in ultracold Fermi gases

We study the collective association dynamics of a cold Fermi gas of 2N atoms in M atomic modes into a single molecular bosonic mode. When the atomic translational motion is slow compared to the atom-molecule conversion rate, the many-body fermionic problem for 2^M amplitudes is effectively reduced to a dynamical system of min{N, M} + 1 amplitudes, making the solution no more complex than the solution of a two-mode Bose-Einstein condensate and allowing realistic calculations with up to 10⁴ particles. The many-body dynamics is shown to be formally similar to the dynamics of the bosonic system under the mapping of boson particles to fermion holes, producing collective enhancement effects due to many-particle constructive interference.     

Quantum field theory with an interaction on the boundary

We consider quantum theory of fields ? defined on a D dimensional manifold (bulk) with an interaction V (?) concentrated on a d < D dimensional surface (brane). Such a quantum field theory can be less singular than the one in d dimensions with an interaction V (?). It is shown that scaling properties of fields on the brane are different from the ones in the bulk. We discuss as an example fields on de Sitter space.     

Dynamics of atom scattering from 4He nanoclusters

We present a microscopic theory and results of atom scattering calculations to determine the dispersion of surface modes (ripplons) of superfluid helium-4 nanodroplets, expanding previous work [J. Chem. Phys. 115, 10161 (2001)]. A quantum transport formalism is adapted to the many-body scattering problem, yielding both elastic and inelastic fluxes. We demonstrate that, in analogy to the dynamic structure function S(k,ω) obtained from neutron scattering, a dynamic structure function σ(k,ω) can be obtained from ³He scattering. The ³He dynamic structure function σ(k,ω) is sensitive to surface dynamics, whereas the neutron dynamic structure function S(k,ω) is dominated by bulk-like excitations, in particular by rotons. Unlike for neutron-scattering, the total inelastic cross section for atom-scattering on ⁴He nanodroplets is large which we believe makes experimental detection feasible. We also show that scattering identical particles, i.e. ⁴He atoms, does not provide information about the dispersion of surface modes. Instead, inelastically scattered ⁴He atoms preferably lose roughly half their energy.     

High Dimensional Atomic States of Hydrogenic Type: Heisenberg-like and Entropic Uncertainty Measures

High dimensional atomic states play a relevant role in a broad range of quantum fields, ranging from atomic and molecular physics to quantum technologies. The D-dimensional hydrogenic system (i.e., a negatively-charged particle moving around a positively charged core under a Coulomb-like potential) is the main prototype of the physics of multidimensional quantum systems. In this work, we review the leading terms of the Heisenberg-like (radial expectation values) and entropy-like (Rényi, Shannon) uncertainty measures of this system at the limit of high D. They are given in a simple compact way in terms of the space dimensionality, the Coulomb strength and the state’s hyperquantum numbers. The associated multidimensional position–momentum uncertainty relations are also revised and compared with those of other relevant systems.     

Self-consistent Overhauser model for the pair distribution function of an electron gas at finite temperature

We present calculations of the spin-averaged pair distribution function g(r) in a homogeneous gas of electrons moving in dimensionality D=3 or D=2 at finite temperature. The model involves the solution of a two-electron scattering problem via an effective potential, which embodies many-body effects through a self-consistent Hartree approximation, leading to two-body wave functions to be averaged over a temperature-dependent distribution of relative momentum for electron pairs. We report illustrative numerical results for g(r) in an intermediate-coupling regime and interpret them in terms of changes of short-range order with increasing temperature.     

0.7 structure in long quantum wires

While quantized conductance steps in short quantum wires are understood through a single electron picture, additional structure often observed in high-quality one-dimensional systems near g=0.7×(2e²/h) is commonly interpreted as arising due to many-body interactions. Most studies of conductance structure below 2e²/h use short one-dimensional wires where transport is known to be ballistic. We report transport measurements for both short (0.5 μm) and long (5 μm) quantum wires, and use both conductance and nonlinear transport to explore the behavior of one-dimensional wires.     

Stability of neutral and negative donor impurity in a semiconductor cylindrical quantum dot

The stability of neutral (D⁰) and negative charged donor (D⁻) on- and off-center in anisotropic cylindrical quantum dot (CQD) is studied by use of a variational approach. Two-parameter anisotropic trial wave function which includes electron-correlation effects is utilized, to explore strong and weak confinement regions. A comparison between one and two-parameter trial wave functions results is introduced. The finite barrier height and the CQD dimensions, dependence of the “stability and the binding energy” of the D⁰ and the D⁻ is obtained. It has been shown that the donor's stability dependent on CQD dimensions and the confinement potential in strong confinement region but in weak confinement region, the stability of D⁰ and D⁻ is dependent strongly on the quantum dot (QD) radius R. It has been found that the donors D⁰ and D⁻ off-center are less stable than the on-center impurities, and also the off-center donors more stable in small CQDs. It has shown that the stability of D⁻ depends on the energy of the excess electron.     

Multipartite entanglement concentration of electron-spin states with CNOT gates

We propose a different entanglement concentration protocol (ECP) for nonlocal N-electron systems in a partially entangled Bell-type pure state using the CNOT gates and the projection measurements on an additional electron. For each nonlocal N-electron system, Alice first entangles it with the additional electron, and then she projects the additional electron onto an orthogonal basis for dividing the N-electron systems into two groups. In the first group, the N parties obtain a subset of N-electron systems in a maximally entangled state directly. In the second group, they obtain some less-entangled N-electron systems, which are the resource for the entanglement concentration in the next round. By iterating the entanglement concentration process several times, the present ECP has the maximal success probability, which is the theoretical limit of an ECP, equal to the entanglement of the partially entangled state, and higher than the others. This ECP may be useful in quantum computers based on electron-spin systems in the future.     

Quantum information entropies of ultracold atomic gases in a harmonic trap

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as S_t^(D) = N(a D - b lnN) S_\mathrm{t}^{(D)} = N(a D - b \ln N) , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.     

Electron capture and scaling anomaly in polar molecules

We present a new analysis of the electron capture mechanism in polar molecules, based on von Neumann's theory of self-adjoint extensions. Our analysis suggests that it is theoretically possible for polar molecules to form bound states with electrons, even with dipole moments smaller than the critical value D₀=1.63×¹⁰⁻¹⁸ esu cm. We argue that the quantum mechanical scaling anomaly is responsible for the formation of these bound states.     

Collective quantum decoherence induced by qubit-electron interaction

We investigate a model of quantum register composed of N qubits coupling with itinerant electrons by adopting the Born-Markov master equation. Decoherence induced by this coupling is studied for various initial states. By solving the master equation for N=4 with the numerical integration, we obtain time evolution of fidelity and linear entropy of the register. The decoherence rate of this model is proportional to ²|J^′| with J^′ being the exchange coupling strength of electrons and qubits. We also investigate the decoherence free subspace which provides a possible routine of applications in quantum computation.     

solitons in quantum Hall systems

We present here an elementary pedagogical introduction to CP_N solitons in quantum Hall systems. We begin with a brief introduction to both CP_N models and to quantum Hall (QH) physics. We then focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact CP_N fields for N = 1 and N = 3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding CP_N field equations. We conclude with a brief summary of our own recent work in this area, done with Sankalpa Ghosh. Received 17 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: doug0700@mail.jnu.ac.in