Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLandauer-Buttiker and Thouless conductance
128
0
0.0
(
0
)
Added by
Claude-Alain Pillet
Publication date
2014
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample S connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer-Buttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of S. In this spirit, we define Landauer-Buttiker crystalline currents by extending the Landauer-Buttiker formula to a setup where the sample S is replaced by a periodic structure whose unit cell is S. We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.
rate research
Read More
In this work, we model the zero-bias conductance for the four different DNA strands that were used in conductance measurement experiment [A. K. Mahapatro, K. J. Jeong, G. U. Lee, and D. B. Janes, Nanotechnology 18, 195202 (2007)]. Our approach consists of three elements: (i) ab initio calculations of DNA, (ii) Greens function approach for transport calculations, and (iii) the use of two parameters to determine the decoherence rates. We first study the role of the backbone. We find that the backbone can alter the coherent transmission significantly at some energy points by interacting with the bases, though the overall shape of the transmission stays similar for the two cases. More importantly, we find that the coherent electrical conductance is tremendously smaller than what the experiments measure. We consider DNA strands under a variety of different experimental conditions and show that even in the most ideal cases, the calculated coherent conductance is much smaller than the experimental conductance. To understand the reasons for this, we carefully look at the effect of decoherence. By including decoherence, we show that our model can rationalize the measured conductance of the four strands, both qualitatively and quantitatively. We find that the effect of decoherence on G:C base pairs is crucial in getting agreement with the experiments. However, the decoherence on G:C base pairs alone does not explain the experimental conductance in strands containing a number of A:T base pairs. Including decoherence on A:T base pairs is also essential. By fitting the experimental trends and magnitudes in the conductance of the four different DNA molecules, we estimate for the first time that the deocherence rate is 6 meV for G:C and 1.5 meV for A:T base pairs.
The quantum fluctuations of the entropy production for fermionic systems in the Landauer-Buttiker non-equilibrium steady state are investigated. The probability distribution, governing these fluctuations, is explicitly derived by means of quantum field theory methods and analysed in the zero frequency limit. It turns out that microscopic processes with positive, vanishing and negative entropy production occur in the system with non-vanishing probability. In spite of this fact, we show that all odd moments (in particular, the mean value of the entropy production) of the above distribution are non-negative. This result extends the second principle of thermodynamics to the quantum fluctuations of the entropy production in the Landauer-Buttiker state. The impact of the time reversal is also discussed.
This paper reviews many of the known inequalities for the eigenvalues of the Laplacian and bi-Laplacian on bounded domains in Euclidean space. In particular, we focus on isoperimetric inequalities for the low eigenvalues of the Dirichlet and Neumann Laplacians and of the vibrating clamped plate problem (i.e., the biharmonic operator with ``Dirichlet boundary conditions). We also discuss the known universal inequalities for the eigenvalues of the Dirichlet Laplacian and the vibrating clamped plate and buckling problems and go on to present some new ones. Some of the names associated with these inequalities are Rayleigh, Faber-Krahn, Szego-Weinberger, Payne-Polya-Weinberger, Sperner, Hile-Protter, and H. C. Yang. Occasionally, we will also comment on extensions of some of our inequalities to bounded domains in other spaces, specifically, S^n or H^n.
This paper is a continuation of my previous work on absolutely continuous and singular spectral shift functions, where it was in particular proved that the singular part of the spectral shift function is an a.e. integer-valued function. It was also shown that the singular spectral shift function is a locally constant function of the coupling constant $r,$ with possible jumps only at resonance points. Main result of this paper asserts that the jump of the singular spectral shift function at a resonance point is equal to the so-called resonance index, --- a new (to the best of my knowledge) notion introduced in this paper. Resonance index can be described as follows. For a fixed $lambda$ the resonance points $r_0$ of a path $H_r$ of self-adjoint operators are real poles of a certain meromorphic function associated with the triple $(lambda+i0; H_0,V).$ When $lambda+i0$ is shifted to $lambda+iy$ with small $y>0,$ that pole get off the real axis in the coupling constant complex plane and, in general, splits into some $N_+$ poles in the upper half-plane and some $N_-$ poles in the lower half-plane (counting multiplicities). Resonance index of the triple $(lambda; H_{r_0},V)$ is the difference $N_+-N_-.$ Based on the theorem just described, a non-trivial example of singular spectral shift function is given.
Given a self-adjoint operator H, a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure is defined such that for all points of this set the wave and the scattering matrices can be defined and constructed unambiguously. Many well-known properties of the wave and scattering matrices and operators are proved, including the stationary formula for the scattering matrix. This new abstract scattering theory allows to prove that for any trace class perturbations of arbitrary self-adjoint operators the singular part of the spectral shift function is an almost everywhere integer-valued function.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
