Confined Harmonically Interacting Spin-Polarized Fermions in a Magnetic Field: Thermodynamics

We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin polarized fermions in a confiment potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three dimensional model of N harmonically interacting spin polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied.Comment: 7 pages REVTEX and 8 postscript figures, accepted in Phys. Rev.

Density of a gas of spin polarized fermions in a magnetic field

For a fermion gas with equally spaced energy levels that is subjected to a magnetic field, the particle density is calculated. The derivation is based on the path integral approach for identical particles, in combination with the inversion techniques for the generating function of the static response functions. Explicit results are presented for the ground state density as a function of the magnetic field with a number of particles ranging from 1 to 45.Comment: 9 pages, 8 figures; To appear in Phys. Rev. E on December 1, 2000; e-mail addresses: [email protected], [email protected], [email protected], [email protected]

Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions

For a fermion gas with equally spaced energy levels, the density and the pair correlation function are obtained. The derivation is based on the path integral approach for identical particles and the inversion of the generating functions for both static responses. The density and the pair correlation function are evaluated explicitly in the ground state of a confined fermion system with a number of particles ranging from 1 to 220 and filling the Fermi level completely.Comment: 11 REVTEX pages, 3 postscript figures. Accepted for publication in Phys. Rev. E, Vol. 58 (August 1, 1998

Dynamic correlations of the Coulomb Luttinger liquid

The dynamic density response function, form-factor, and spectral function of a Luttinger liquid with Coulomb electron-electron interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The form of the density response function is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic form-factor contains the $\delta$-peak in the long-wave region, corresponding to one-boson excitations. Besides, the multi-boson-excitations band exists in the wave-number region near to $2k_F$. The dynamic form-factor diverges at the edges of this band, while the dielectric function goes to zero there, which indicates the appearance of a soft mode. We develop a method to analyze the asymptotics of the spectral functions near to the edges of the multi-boson-excitations band.Comment: 11 pages, 3 figures, submitted to PR

Condensation and interaction range in harmonic boson traps: a variational approach

For a gas of N bosons interacting through a two-body Morse potential a variational bound of the free energy of a confined system is obtained. The calculation method is based on the Feynman-Kac functional projected on the symmetric representation. Within the harmonic approximation a variational estimate of the effect of the interaction range on the existence of many-particle bound states, and on the N-T phase diagram is obtained.Comment: 14 pages+4 figures, submitted to phys.rev.

Bipolaron Binding in Quantum Wires

A theory of bipolaron states in quantum wires with a parabolic potential well is developed applying the Feynman variational principle. The basic parameters of the bipolaron ground state (the binding energy, the number of phonons in the bipolaron cloud, the effective mass, and the bipolaron radius) are studied as a function of sizes of the potential well. Two cases are considered in detail: a cylindrical quantum wire and a planar quantum wire. Analytical expressions for the bipolaron parameters are obtained at large and small sizes of the quantum well. It is shown that at $R\gg 1$ [where $R$ means the radius (halfwidth) of a cylindrical (planar) quantum wire, expressed in Feynman units], the influence of confinement on the bipolaron binding energy is described by the function $\sim 1/R^{2}$ for both cases, while at small sizes this influence is different in each case. In quantum wires, the bipolaron binding energy $W(R)$ increases logarithmically with decreasing radius. The shapes and the sizes of a nanostructure, which are favorable for observation of stable bipolaron states, are determined.Comment: 17 pages, 6 figures, E-mail addresses: [email protected]; [email protected]

Ground-State of Charged Bosons Confined in a Harmonic Trap

We study a system composed of N identical charged bosons confined in a harmonic trap. Upper and lower energy bounds are given. It is shown in the large N limit that the ground-state energy is determined within an accuracy of $\pm 8$ and that the mean field theory provides a reasonable result with relative error of less than 16% for the binding energy .Comment: 15 page

Endoscopic submucosal dissection for early esophageal squamous cell carcinoma:long-term results from a Western cohort

Background Although endoscopic submucosal dissection (ESD) is established as first-choice treatment for early esophageal squamous cell carcinoma (ESCC) worldwide, most data are derived from Asian studies. We aimed to evaluate the long-term outcomes of ESD for patients with early ESCC in a Western cohort. Methods In this retrospective cohort study, patients with early ESCC amenable to ESD were included from four tertiary referral hospitals in the Netherlands between 2012 and 2017. All ESD procedures were performed by experienced endoscopists, after which the decision for additional treatment was made on a per-patient basis. Outcomes were curative resection rate, ESCC-specific survival, and overall survival. Results Of 68 included patients (mean age 69 years; 34 males), ESD was technically successful in 66 (97%; 95%CI 93%-100%), with curative resection achieved in 34/66 (52%; 95%CI 39%-64%). Among patients with noncurative resection, 15/32 (47%) underwent additional treatment, mainly esophagectomy (n = 10) or definitive chemoradiation therapy (n = 4). Endoscopic surveillance was preferred in 17/32 patients (53%), based on severe comorbidities or patient choice. Overall, 31/66 patients (47%) died during a median follow-up of 66 months; 8/31 (26%) were ESCC-related deaths. The 5-year overall and ESCC-specific survival probabilities were 62% (95%CI 52%-75%) and 86% (95%CI 77%-96%), respectively. Conclusion In this Western cohort with long-term follow-up, the effectiveness and safety of ESD for early ESCC was confirmed, although the rate of noncurative resections was substantial. Irrespective of curative status, the long-term prognosis of these patients was limited mainly due to competing mortality

Do attractive bosons condense?

Motivated by experiments on bose atoms in traps which have attractive interactions (e.g. ^7Li), we consider two models which may be solved exactly. We construct the ground states subject to the constraint that the system is rotating with angular momentum proportional to the number of atoms. In a conventional system this would lead to quantised vortices; here, for attractive interactions, we find that the angular momentum is absorbed by the centre of mass motion. Moreover, the state is uncondensed and is an example of a `fragmented' condensate discussed by Nozi\`eres and Saint James. The same models with repulsive interactions are fully condensed in the thermodynamic limit.Comment: 4 pages, Latex, RevTe

Bose-Einstein condensation in a one-dimensional interacting system due to power-law trapping potentials

We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the Gross-Pitaevskii equation within the semi-classical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for finite number of particles at low temperature indicating a phase transition for weakly interacting systems.Comment: LaTeX, 6 pages, 8 figures, uses grafik.sty (included), to be published in Phys. Rev.