Related Experiment Video
Updated: May 21, 2026
11:21
Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
Published on: March 30, 2017
Boltzmann-type approach to transport in weakly interacting one-dimensional fermionic systems
Christian Bartsch1, Jochen Gemmer
1Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, D-49069 Osnabrück, Germany.
Summary
We studied one-dimensional fermionic models with interactions and hopping. Our findings suggest anomalous diffusive transport behavior in certain nonintegrable cases, revealing slow current relaxation.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Statistical mechanics
Background:
- One-dimensional (1D) systems exhibit unique quantum phenomena.
- Fermionic tight-binding models are crucial for understanding electron behavior in solids.
- Interactions and longer-range hopping can significantly alter transport properties.
Purpose of the Study:
- To investigate the transport properties of 1D fermionic tight-binding models.
- To analyze the impact of nearest and next-nearest neighbor hopping on diffusion.
- To explore the role of weak short-range mutual interactions.
Main Methods:
- Utilizing a projection operator method to map Schrödinger dynamics.
- Deriving a linear quantum Boltzmann equation from the model.
- Numerically obtaining diffusion coefficients for nonintegrable cases.
- Analytically investigating current decay behavior in the integrable case.
Main Results:
- Diffusion coefficients were numerically obtained for nonvanishing next-nearest neighbor hopping (nonintegrable case).
- The diffusion coefficient diverges in the absence of next-nearest neighbor hopping (integrable case).
- Slow current relaxation was observed for arbitrarily small current components in the integrable case.
Conclusions:
- The study suggests anomalous diffusive transport behavior in 1D fermionic models with specific hopping parameters.
- The quantum Boltzmann equation approach provides a viable method for analyzing such systems.
- The presence or absence of next-nearest neighbor hopping fundamentally changes the transport characteristics.
Related Concept Videos
01:21Carrier Transport
The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
01:28Debye–Huckel–Onsager Conductance Equation
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
01:20Maxwell-Boltzmann Distribution: Problem Solving
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
01:29Kohlraush’s Law and its Applications
Kohlrausch's law explains that at infinite dilution, where dissociation is complete, each ion's contribution to the conductivity of the electrolyte is independent of the nature of other ions present in the solution. It also implies that when an electrolyte is highly diluted, the conductance of the electrolyte is the sum of the individual conductances of the ions it generates upon dissociation. The quantity of electricity an ion carries is proportional to its molar ionic conductance, which...
02:32The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
01:31Transport Number
The transport number is the fraction of the total current carried by an ion in an electrolyte solution. It is defined as the ratio of the current carried by a specific ion to the total current flowing through the solution. The transport number, t, is central to understanding ionic mobility, which describes how fast an ion moves under the influence of an electric field. This link connects the physical behavior of ions in solution to the chemical processes that occur during electrochemical...