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We study non-equilibrium steady state transport in scale invariant quantum junctions with focus on the particle and heat fluctuations captured by the two-point current correlation functions. We show that the non-linear behavior of the particle current affects both the particle and heat noise. The existence of domains of enhancement and reduction of the noise power with respect to the linear regime are observed. The impact of the statistics is explored. We demonstrate that in the scale invariant case the bosonic particle noise exceeds the fermionic one in the common domain of heat bath parameters. Multi-lead configurations are also investigated and the effect of probe terminals on the noise is discussed.
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We derive the efficiency at maximal power of a scale-invariant (critical) quantum junction in exact form. Both Fermi and Bose statistics are considered. We show that time-reversal invariance is spontaneously broken. For fermions we implement a new mechanism for efficiency enhancement above the Curzon-Ahlborn bound, based on a shift of the particle energy in each heat reservoir, proportional to its temperature. In this setting fermionic junctions can even reach at maximal power the Carnot efficiency. The bosonic junctions at maximal power turn out to be less efficient then the fermionic ones.
The power spectrum of quantum dot fluorescence exhibits $1/f^beta$ noise, related to the intermittency of these nanosystems. As in other systems exhibiting $1/f$ noise, this power spectrum is not integrable at low frequencies, which appears to imply infinite total power. We report measurements of individual quantum dots that address this long-standing paradox. We find that the level of $1/f^beta$ noise decays with the observation time. The change of the spectrum with time places a bound on the total power. These observations are in stark contrast with most measurements of noise in macroscopic systems which do not exhibit any evidence for non-stationarity. We show that the traditional description of the power spectrum with a single exponent $beta$ is incomplete and three additional critical exponents characterize the dependence on experimental time.
Invariant ensembles of random matrices are characterized by the distribution of their eigenvalues ${lambda_1,cdots,lambda_N}$. We study the distribution of truncated linear statistics of the form $tilde{L}=sum_{i=1}^p f(lambda_i)$ with $p<N$. This problem has been considered by us in a previous paper when the $p$ eigenvalues are further constrained to be the largest ones (or the smallest). In this second paper we consider the same problem without this restriction which leads to a rather different analysis. We introduce a new ensemble which is related, but not equivalent, to the thinned ensembles introduced by Bohigas and Pato. This question is motivated by the study of partial sums of proper time delays in chaotic quantum dots, which are characteristic times of the scattering process. Using the Coulomb gas technique, we derive the large deviation function for $tilde{L}$. Large deviations of linear statistics $L=sum_{i=1}^N f(lambda_i)$ are usually dominated by the energy of the Coulomb gas, which scales as $sim N^2$, implying that the relative fluctuations are of order $1/N$. For the truncated linear statistics considered here, there is a whole region (including the typical fluctuations region), where the energy of the Coulomb gas is frozen and the large deviation function is purely controlled by an entropic effect. Because the entropy scales as $sim N$, the relative fluctuations are of order $1/sqrt{N}$. Our analysis relies on the mapping on a problem of $p$ fictitious non-interacting fermions in $N$ energy levels, which can exhibit both positive and negative effective (absolute) temperatures. We determine the large deviation function characterizing the distribution of the truncated linear statistics, and show that, for the case considered here ($f(lambda)=1/lambda$), the corresponding phase diagram is separated in three different phases.
The impact of bound states in Landauer-Buttiker scattering approach to non-equilibrium quantum transport is investigated. We show that the noise power at frequency $ u$ is sensitive to all bound states with energies $omega_b$ satisfying $|omega_b| < u$. We derive the exact expression of the bound state contribution and compare it to the one produced by the scattering states alone. It turns out that the bound states lead to specific modifications of both space and frequency dependence of the total noise power. The theoretical and experimental consequences of this result are discussed.
This paper deal the effects of uncorrelated white noise, in a serie of Josephson Junctions coupled to a linear $RLC$ resonator. The junction are hysteretic, and hence can be considered birhythmic, that is capable to oscillate at different frequencies for the same set of parameters. Both Josephson Junctions with identical and disordered parameters are considered. With the uniform parameters, the array behaves similarly to single Josephson junctions, also in the presence of noise. The magnitude of the effective energy that characterizes the response to noise becomes smaller as the number of elements of the array increases, making the resonator less stable. Disorder in the parameters drastically changes the physics of the array. The disordered array of Josephson junctions misses the birhythmicity properties for large values of the variance of the disorder parameter. Nevertheless, the system remains birhythmic for low values of the disorder parameter. Finally, disorder makes it difficult to locate the separatrix, hinting to a more complex structure of the effective energy landscape.
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