By Daniel Waltner
This quantity describes mesoscopic platforms with classically chaotic dynamics utilizing semiclassical equipment which mix components of classical dynamics and quantum interference results. Experiments and numerical reports exhibit that Random Matrix thought (RMT) explains actual houses of those platforms good. This was once conjectured greater than 25 years in the past by means of Bohigas, Giannoni and Schmit for the spectral homes. on account that then, it's been a problem to appreciate this connection analytically.
The writer bargains his readers a clearly-written and up to date remedy of the subjects coated. He extends earlier semiclassical techniques that handled spectral and conductance houses. He indicates that RMT effects can regularly purely be received semiclassically while taking into consideration classical configurations no longer thought of formerly, for instance these containing multiply traversed periodic orbits.
Furthermore, semiclassics is able to describing results past RMT. during this context he stories the impact of a non-zero Ehrenfest time, that is the minimum time wanted for an at the beginning spatially localized wave packet to teach interference. He derives its signature on a number of amounts characterizing mesoscopic platforms, e. g. dc and ac conductance, dc conductance variance, n-pair correlation capabilities of scattering matrices and the distance within the density of states of Andreev billiards.
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Extra info for Semiclassical Approach to Mesoscopic Systems: Classical Trajectory Correlations and Wave Interference
E. the classical survival probability ρcl (t) is equal to the quantum one ρqm (t). Turning now D. 1007/978-3-642-24528-2_3, © Springer-Verlag Berlin Heidelberg 2012 41 42 3 Survival Probability and Fidelity Decay to an open system, ρqm (t) can deviate from its classical counterpart, ρcl (t). We can thus get access to quantum properties by opening up the system and comparing ρcl (t) and ρqm (t). As already given in the last chapter after Eq. 2) with the classical dwell time τD = Ω/(2π N) obtained in the case of N open channels.
32). e. e. λτ D → ∞. Additionally we assume 2mλ / p 2 λτ D ≈ 1; we will return to the last point in Chap. 37). 1 Magnetic Field Dependence of the Non-diagonal Contribution Up to now we assumed time-reversal symmetry. If this symmetry is destroyed, for example by applying a strong magnetic field, the latter contribution will vanish, because the closed loop has to be traversed in different directions by the trajectory and its partner. Here we study the transition region between zero and weak magnetic field.
Before deriving the number of self-crossings, P ( , T ) d , in the range between and + d for an orbit of time T, we give rough arguments how this expression depends on and T for trajectories in billiards. There, each orbit is composed of a chain of N chords connecting the reflection points. 3 Quantum Corrections to the Transmission 25 chords cannot intersect, the third chord can cross with up to one, the fourth chord with up to two segments, and so on. e. proportional to T 2 . be proportional to n=3 The crossing-angle dependence of P ( , T ) can be estimated for small as follows: Given a trajectory chord of length L , a second chord, tilted by an angle with respect to the first one, will cross it inside the billiard (with area of order L 2 ) only if the distance between the reflection points of the two chords at the boundary is smaller than L sin .
Semiclassical Approach to Mesoscopic Systems: Classical Trajectory Correlations and Wave Interference by Daniel Waltner