scholarly journals Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential

2015 ◽  
Vol 1 (6) ◽  
pp. e1500197 ◽  
Author(s):  
Jesper Levinsen ◽  
Pietro Massignan ◽  
Georg M. Bruun ◽  
Meera M. Parish
Keyword(s):  
Fermi Gas ◽  
Harmonic Potential ◽  
Chain Model ◽  
Many Body ◽  
Exact Methods ◽  
One Dimensional ◽  
Heisenberg Spin Chain ◽  
Precise Knowledge ◽  
Short Range Repulsion ◽  
The One

A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascal’s triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.

scholarly journals Anomalous Diffusion with an Apparently Negative Diffusion Coefficient in a One-Dimensional Quantum Molecular Chain Model

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 506
Author(s):  
Sho Nakade ◽  
Kazuki Kanki ◽  
Satoshi Tanaka ◽  
Tomio Petrosky
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Constant ◽  
Mean Square Displacement ◽  
Second Law Of Thermodynamics ◽  
Molecular Chain ◽  
Chain Model ◽  
Phase Mixing ◽  
One Dimensional ◽  
The One ◽  
Negative Diffusion

An interesting anomaly in the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

scholarly journals Probing non-thermal density fluctuations in the one-dimensional Bose gas

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Jacopo De Nardis ◽  
Milosz Panfil ◽  
Andrea Gambassi ◽  
Leticia Cugliandolo ◽  
Robert Konik ◽  
...  
Keyword(s):  
Spatial Dimension ◽  
Bose Gas ◽  
Density Fluctuations ◽  
Dynamical Structure ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Fluctuation Dissipation ◽  
Quantum Integrable Models ◽  
The One

Quantum integrable models display a rich variety of non-thermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a many-body initial state unitarily evolve with an integrable Hamiltonian. At late times these systems are locally described by a generalized Gibbs ensemble with as many effective temperatures as their local conserved quantities. The experimental measurement of this macroscopic number of temperatures remains elusive. Here we show that they can be obtained for the Bose gas in one spatial dimension by probing the dynamical structure factor of the system after the quench and by employing a generalized fluctuation-dissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from state-of-the-art experimental observations.

ESR Study of Electrochemically Doped Chalcogenide Nanotubes

2003 ◽  
Vol 775 ◽  
Author(s):  
Denis Arcon ◽  
Andrej Zorko ◽  
Pavel Cevc ◽  
Ales Mrzel ◽  
Maja Remskar ◽  
...  
Keyword(s):  
Room Temperature ◽  
Electrochemical Activity ◽  
Chain Model ◽  
Heisenberg Chain ◽  
One Dimensional ◽  
Narrow Component ◽  
Broad Component ◽  
X Band ◽  
Heavily Doped ◽  
The One

AbstractElectrochemical activity of differently pretreated single-wall subnanometer-diameter molybdenum disulfide tubes (nMoS2) was tested and compared with layered MoS2 material. In as prepared and de-iodized nMoS2 samples a significant increase in the charge capacity has been found compared to the one measured in dispersed nMoS2 or layered MoS2. Enhanced electrochemical activity has been attributed to a particular one-dimensional topology of nanotubes bundles. Electrochemically doped samples were then studied with X-band ESR. While undoped nMoS2 show no X-band ESR signal between room temperature and 4 K we found in heavily doped nMoS2 samples two distinct ESR components: a narrow component with a linewidth of few Guass and a broad component with a linewidth of more than 800 G. The broad ESR component is characteristic of Mo d-orbital-derived band. The temperature dependence of the ESR spin susceptibility and the linewidth of the broad ESR component can be discussed either in terms of conducting electrons coupled to defects or in terms of random-exchange Mo Heisenberg chain model.

scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

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