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61.
We study the interplay of charge and spin (zero-mode) channels in quantum dots. The latter affects the former in the form of a distinct signature on the differential conductance. We also obtain both longitudinal and transverse spin susceptibilities. All these observables, underlain by spin fluctuations, become accentuated as one approaches the Stoner instability. The nonperturbative effects of zero-mode interaction are described in terms of the propagation of gauge bosons associated with charge [U(1)] and spin [SU(2)] fluctuations in the dot, while transverse spin fluctuations are analyzed perturbatively. 相似文献
62.
Yuval Berg Sharone Goldring Shaul Pearl Ady Arie 《Applied physics. B, Lasers and optics》2013,111(3):425-428
A new method for Q-switching an all-fiber laser is presented. It is based on induced acoustic long period grating operating on a null coupler, which acts as acoustically controlled tunable output coupler. Q-switching is achieved by switching on and off the acoustic wave in a burst mode, thereby generating laser pulses that are ~400 times shorter than the acoustically controlled coupler’s rise time. Output pulse energy of 22 μJ and temporal width of ~100 ns were measured at a wavelength of 1.54 μm. 相似文献
63.
We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure. 相似文献
64.
We consider Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss model. It is well-known that the mixing-time in the high temperature regime (β < 1) has order n log n, whereas the mixing-time in the case β > 1 is exponential in n. Recently, Levin, Luczak and Peres proved that for any fixed β < 1 there is cutoff at time with a window of order n, whereas the mixing-time at the critical temperature β = 1 is Θ(n
3/2). It is natural to ask how the mixing-time transitions from Θ(n log n) to Θ(n
3/2) and finally to exp (Θ(n)). That is, how does the mixing-time behave when β = β(n) is allowed to tend to 1 as n → ∞. In this work, we obtain a complete characterization of the mixing-time of the dynamics as a function of the temperature,
as it approaches its critical point β
c
= 1. In particular, we find a scaling window of order around the critical temperature. In the high temperature regime, β = 1 − δ for some 0 < δ < 1 so that δ
2
n → ∞ with n, the mixing-time has order (n/δ) log(δ
2
n), and exhibits cutoff with constant and window size n/δ. In the critical window, β = 1± δ, where δ
2
n is O(1), there is no cutoff, and the mixing-time has order n
3/2. At low temperature, β = 1 + δ for δ > 0 with δ
2
n → ∞ and δ = o(1), there is no cutoff, and the mixing time has order .
Research of J. Ding and Y. Peres was supported in part by NSF grant DMS-0605166. 相似文献
65.
Diffusion describes the stochastic motion of particles and is often a key factor in determining the functionality of materials. Modeling diffusion of atoms can be very challenging for heterogeneous systems with high energy barriers. In this report, popular computational methodologies are covered to study diffusion mechanisms that are widely used in the community and both their strengths and weaknesses are presented. In static approaches, such as electronic structure theory, diffusion mechanisms are usually analyzed within the nudged elastic band (NEB) framework on the ground electronic surface usually obtained from a density functional theory (DFT) calculation. Another common approach to study diffusion mechanisms is based on molecular dynamics (MD) where the equations of motion are solved for every time step for all the atoms in the system. Unfortunately, both the static and dynamic approaches have inherent limitations that restrict the classes of diffusive systems that can be efficiently treated. Such limitations could be remedied by exploiting recent advances in artificial intelligence and machine learning techniques. Here, the most promising approaches in this emerging field for modeling diffusion are reported. It is believed that these knowledge‐intensive methods have a bright future ahead for the study of diffusion mechanisms in advanced functional materials. 相似文献
66.
Stability testing of two-dimensional (2-D) discrete-time systems requires decision on whether a 2-D (bivariate) polynomial does not vanish in the closed exterior of the unit bi-circle. The paper reformulates a tabular test advanced by Jury to solve this problem. The 2-D tabular test builds for a real 2-D polynomial of degree (n
1, n
2) a sequence of n
2 matrices or 2-D polynomials (the 2-D table). It then examines its last polynomial - a 1-D polynomial of degree 2n
1
n
2 - for no zeros on the unit circle. A count of arithmetic operations for the tabular test is performed. It shows that the test has O(n
6) complexity (assuming n
1 = n
2 = n)- a significant improvement compared to previous tabular tests that used to be of exponential complexity. The analysis also reveals that, even though the testing of the condition on the last polynomial requires O(n
4) operations, the count of operations required for the table's construction makes the overall complexity O(n
6). Next it is shown that it is possible to telescope the last polynomial of the table by interpolation and circumvent the construction of the 2-D table. The telepolation of the tabular test replaces the table by n
1
n
2 + 1 stability tests of 1-D polynomials of degree n
1 or n
2 of certain form. The resulting new 2-D stability testing procedure requires a very low O(n
4) count of operations. The paper also brings extension for the tabular test and its simplification by telepolation to testing 2-D polynomials with complex valued coefficients. 相似文献
67.
We consider biased random walk on supercritical percolation clusters in ℤ2. We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random
walk has speed zero, while if the bias is small enough, the speed of the random walk is positive.
Received: 20 November 2002 / Revised version: 17 January 2003
Published online: 15 April 2003
Research supported by Microsoft Research graduate fellowship.
Research partially supported by the DFG under grant SPP 1033.
Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley.
Mathematics Subject Classification (2000): 60K37; 60K35; 60G50
Key words or phrases: Percolation – Random walk 相似文献
68.
The number of infinite clusters in dynamical percolation 总被引:2,自引:2,他引:0
Summary. Dynamical percolation is a Markov process on the space of subgraphs of a given graph, that has the usual percolation measure
as its stationary distribution. In previous work with O. H?ggstr?m, we found conditions for existence of infinite clusters
at exceptional times. Here we show that for ℤ
d
, with p>p
c
, a.s. simultaneously for all times there is a unique infinite cluster, and the density of this cluster is θ(p). For dynamical percolation on a general tree Γ, we show that for p>p
c
, a.s. there are infinitely many infinite clusters at all times. At the critical value p=p
c
, the number of infinite clusters may vary, and exhibits surprisingly rich behaviour. For spherically symmetric trees, we
find the Hausdorff dimension of the set T
k
of times where the number of infinite clusters is k, and obtain sharp capacity criteria for a given time set to intersect T
k
. The proof of this capacity criterion is based on a new kernel truncation technique.
Received: 5 May 1997 / In revised form: 24 November 1997 相似文献
69.
Yuval Peres 《Israel Journal of Mathematics》1996,95(1):341-347
Say that a sequenceS
0, ..., Sn has a (global) point of increase atk ifS
k is maximal amongS
0, ..., Sk and minimal amongS
k, ..., Sn. We give an elementary proof that ann-step symmetric random walk on the line has a (global) point of increase with probability comparable to 1/logn. (No moment assumptions are needed.) This implies the classical fact, due to Dvoretzky, Erdős and Kakutani (1961), that Brownian
motion has no points of increase.
Research partially supported by NSF grant # DMS-9404391. 相似文献
70.
Yuval Ne’eman 《Acta Physica Hungarica A》2004,19(3-4):241-246
I trace the evolution of the scientific world view in general and of the variational approach specifically, including transformation groups I then review the impact of these ideas at the atomic, nuclear and particle levels. 相似文献