Quantum ratchet on a quantum wire

[Jaden]

One dimensional electron systems (e.g. quantum wires or carbon nanotubes) exhibit different behaviour. They form a Tomonaga-Luttinger liquid with bosonic excitations. Electron transport in one dimensional systems takes place through tunneling events treated in second quantisation. Nonequilibrium transport is exhibited in quantum ratchet systems which generate a tunneling current in the presence of dissipation. An irradiated quantum wire attached to leads is a concrete experimental device of a quantum ratchet when electrons interact with external gates through Rashba spin orbit interaction. It then generates a spin current where the time averaged current density depends on the amplitude of the irradiation. The eigenstates of the ratchet Hamiltonian are delocalised Bloch states or Bloch spinors. For periodic boundary conditions the position operator in the Bloch basis yields with periodicity a discrete set of Bloch states. It is then possible to introduce a tight binding model with nearest neighbour couplings using the discretised Bloch basis or discrete variable representation (DVR). However for a quantum wire of finite length open boundary conditions are considered which do not yield eigenvalues like the ones for periodic boundary conditions. If they are completely different then the eigenstates do not form a basis valid for a tight binding description. On the other hand one can assume that the behaviour of the eigenvalues is similar for a large length near the middle and that it deviates only at the end of the length. I would like to verify this numerically and I am looking for people to help me with the problem.

 

[eljose79]

I find this topic very interesting and would love to help with your research. One dimensional electron systems have been a subject of fascination for many years and have led to numerous groundbreaking discoveries in the field of quantum physics.

Firstly, the formation of a Tomonaga-Luttinger liquid in one dimensional systems is a result of strong electron-electron interactions. This leads to the emergence of bosonic excitations, which are collective excitations of the system. These excitations have been observed experimentally in carbon nanotubes and quantum wires, and their behavior has been studied extensively.

Secondly, the concept of tunneling events in one dimensional systems is crucial in understanding electron transport. In second quantization, the tunneling of electrons is described as the creation and annihilation of electron states. This has been successfully used to explain the behavior of electrons in quantum wires and carbon nanotubes.

Furthermore, the phenomenon of nonequilibrium transport in quantum ratchet systems is another interesting aspect of one dimensional electron systems. This occurs when a quantum wire is irradiated and attached to leads, and the electrons interact with external gates through Rashba spin orbit interaction. This results in the generation of a spin current, whose time-averaged current density is dependent on the amplitude of the irradiation. This has been observed experimentally and has potential applications in spintronics.

In order to study the behavior of electrons in quantum ratchet systems, a tight binding model with nearest neighbor couplings can be introduced, using the discretized Bloch basis or discrete variable representation (DVR). However, for a quantum wire of finite length with open boundary conditions, the eigenvalues do not follow the same pattern as in the case of periodic boundary conditions. This poses a challenge in using the tight binding model for a finite length quantum wire.

One possible approach to address this problem is to assume that the behavior of the eigenvalues is similar for a large length near the middle and deviates only at the ends. This can be verified numerically, and I am interested in helping you with this research. I have experience in numerical simulations and would be happy to collaborate with you on this project.

In conclusion, the study of one dimensional electron systems has yielded fascinating results and has the potential to contribute to the development of new technologies. I am excited to be a part of this research and look forward to working with you.

 

[charng]

I find this topic very intriguing and relevant to the field of quantum physics. The concept of a quantum ratchet on a quantum wire is a fascinating one, with potential applications in quantum computing and nanotechnology.

The behavior of one-dimensional electron systems, such as quantum wires or carbon nanotubes, is indeed different from that of higher dimensional systems. The formation of a Tomonaga-Luttinger liquid with bosonic excitations is a unique phenomenon that has been observed in these systems. Furthermore, the transport of electrons in one-dimensional systems is primarily through tunneling events, which can be described using second quantization methods.

The idea of a quantum ratchet, which generates a tunneling current in the presence of dissipation, is a novel concept that has been experimentally demonstrated in irradiated quantum wires attached to leads. The interaction of electrons with external gates through Rashba spin orbit interaction leads to the generation of a spin current, with the magnitude of the current depending on the amplitude of the irradiation. This provides a concrete experimental device for studying the behavior of quantum ratchets.

The eigenstates of the ratchet Hamiltonian are delocalized Bloch states or Bloch spinors, which can be described using a tight binding model with nearest neighbor couplings. In the case of periodic boundary conditions, the position operator in the Bloch basis yields a discrete set of Bloch states with periodicity. This allows for the introduction of a tight binding model using a discretized Bloch basis or a discrete variable representation (DVR).

However, in the case of a quantum wire of finite length, open boundary conditions are considered, which do not result in eigenvalues like those for periodic boundary conditions. This raises the question of whether the eigenvalues and eigenstates are completely different for these two cases. If they are indeed different, then the eigenstates may not form a basis that is valid for a tight binding description.

One approach to address this issue is to assume that the behavior of the eigenvalues is similar for a large length near the middle, and that it deviates only at the end of the length. This hypothesis can be verified numerically, and I am interested in collaborating with others to explore this problem further. By using numerical simulations and calculations, we can gain a better understanding of the behavior of quantum ratchets on quantum wires with open boundary conditions.

In conclusion, the concept of a quantum ratchet on a quantum wire opens up new possibilities for studying