Resummation and the semiclassical theory of spectral statistics

We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation formalism that explicitly preserves the unitarity of the quantum time evolution by incorporating duality relations between short and long classical orbits. This allows us to obtain both the non-oscillatory and the oscillatory contributions to spectral correlation functions within a unified framework, thus overcoming a significant problem in previous approaches. In addition, our results extend beyond the universal regime to describe the system-specific approach to the semiclassical limit.Comment: 10 pages, no figure

The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. Moreover, we describe an algorithm to compute $\mu$

Electronic phase separation due to magnetic polaron formation in the semimetallic ferromagnet EuB6_6 - A weakly-nonlinear-transport study

We report measurements of weakly nonlinear electronic transport, as measured by third-harmonic voltage generation $V_{3\omega}$, in the low-carrier density semimetallic ferromagnet EuB$_6$, which exhibits an unusual magnetic ordering with two consecutive transitions at $T_{c_1} = 15.6$\,K and $T_{c_2} = 12.5$\,K. Upon cooling in zero magnetic field through the ferromagnetic transition, the dramatic drop in the linear resistivity at the upper transition $T_{c_1}$ coincides with the onset of nonlinearity, and upon further cooling is followed by a pronounced peak in $V_{3 \omega}$ at the lower transition $T_{c_2}$. Likewise, in the paramagnetic regime, a drop of the material's magnetoresistance $R(H)$ precedes a magnetic-field-induced peak in nonlinear transport. A striking observation is a linear temperature dependence of $V_{3\omega}^{\rm peak}(H)$. We suggest a picture where at the upper transition $T_{c_1}$ the coalescing MP form a conducting path giving rise to a strong decrease in the resistance. The MP formation sets in at around $T^\ast \sim 35$\,K below which these entities are isolated and strongly fluctuating, while growing in number. The MP then start to form links at $T_{c_1}$, where percolative electronic transport is observed. The MP merge and start forming a continuum at the threshold $T_{c_2}$. In the paramagnetic temperature regime $T_{c_1} < T < T^\ast$, MP percolation is induced by a magnetic field, and the threshold accompanied by charge carrier delocalization occurs at a single critical magnetization.Comment: to appear in J. Kor. Phys. Soc (ICM2012 conference contribution

Towards Baxter equation in supersymmetric Yang-Mills theories

We perform an explicit two-loop calculation of the dilatation operator acting on single trace Wilson operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in N=2 and N=4 supersymmetric Yang-Mills theories. We demonstrate that its eigenspectrum exhibits double degeneracy of opposite parity eigenstates which suggests that the two-loop dilatation operator is integrable. Moreover, the two-loop anomalous dimensions in the two theories differ from each other by an overall normalization factor indicating that the phenomenon is not sensitive to the presence of the conformal symmetry. Relying on these findings, we try to uncover integrable structures behind the two-loop dilatation operator using the method of the Baxter Q-operator. We propose a deformed Baxter equation which exactly encodes the spectrum of two-loop anomalous dimensions and argue that it correctly incorporates a peculiar feature of conformal scalar operators -- the conformal SL(2) spin of such operators is modified in higher loops by an amount proportional to their anomalous dimension. From the point of view of spin chains this property implies that the underlying integrable model is ``self-tuned'' -- the all-loop Hamiltonian of the spin chain depends on the total SL(2) spin which in its turn is proportional to the Hamiltonian.Comment: Latex, 18 pages, 3 figure

The measurement postulates of quantum mechanics are operationally redundant

Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for assigning outcome probabilities (Born's rule) and the post-measurement state-update rule, can be deduced from the other quantum postulates, often referred to as "unitary quantum mechanics", and the assumption that ensembles on finite-dimensional Hilbert spaces are characterised by finitely many parameters. This is achieved by taking an operational approach to physical theories, and using the fact that the manner in which a physical system is partitioned into subsystems is a subjective choice of the observer, and hence should not affect the predictions of the theory. In contrast to other approaches, our result does not assume that measurements are related to operators or bases, it does not rely on the universality of quantum mechanics, and it is independent of the interpretation of probability.Comment: This is a post-peer-review, pre-copyedit version of an article published in Nature Communications. The final authenticated version is available online at: http://dx.doi.org/10.1038/s41467-019-09348-

Lateral Chirality-sorting Optical Spin Forces in Evanescent Fields

The transverse component of the spin angular momentum of evanescent waves gives rise to lateral optical forces on chiral particles, which have the unusual property of acting in a direction in which there is neither a field gradient nor wave propagation. As their direction and strength depends on the chiral polarizability of the particle, they act as chirality-sorting and may offer a mechanism for passive chirality spectroscopy. The absolute strength of the forces also substantially exceeds that of other recently predicted sideways optical forces, such that they may more readily offer an experimental confirmation of the phenomenon.Comment: 7 pages, 2 Figure