Related papers: A New Determinant for Quantum Chaos

Prequantum dynamics has been introduced in the 70' by Kostant-Souriau-Kirillov as an intermediate between classical and quantum dynamics. In common with the classical dynamics, prequantum dynamics transports functions on phase space, but…

We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function w. For a specific choice of w, this kernel describes bulk statistics of finite temperature free fermions. We…

We consider the convergence of additive functionals under the determinantal point process with the confluent hypergeometric kernel, corresponding to a sufficiently smooth function $f(x/R)$, as $R\to\infty$. We show that these functionals…

For a particular class of integral operators $K$ we show that the quantity \[\ph:=\log \det (I+K)-\log \det (I-K)\] satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

In a previous paper [KT] we introduced determinant of the Riemann operator on Quillen's higher $K$-groups of the integer ring of an algebraic number field $K$. We showed that the determinant expresses essentially the inverse of the so…

Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…

Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In…

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…

A numerical study of the quantum double pendulum is conducted. A suitable quantum scaling is found which allows to have as the only parameters the ratios of the lengths and masses of the two pendula and a (quantum) gravity parameter…

For an $m$-summable operator $A$ in a separable Hilbert space the higher regularized Fredholm determinant $\det\nolimits_m(I+A)$ generalizes the classical Fredholm determinant. Recently, Britz et al presented a proof of a product formula \[…

Time dependent quadratic Hamiltonians are well known as well in classical mechanics and in quantum mechanics. In particular for them the correspondance between classical and quantum mechanics is exact. But explicit formulas are non trivial…

Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…

The concept of determinant for a linear operator in an infinite-dimensional space is addressed, by using the derivative of the operator's zeta-function (following Ray and Singer) and, eventually, through its zeta-function trace. A little…

We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient…

Based on periodic orbit theory we address the individual-system versus ensemble interpretation of quantum gravity from a quantum chaos perspective. To this end we show that the spectrum of geodesic motion on high-dimensional hyperbolic…

We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different…

We semiclassically derive the leading off-diagonal correction to the spectral form factor of quantum systems with a chaotic classical counterpart. To this end we present a phase space generalization of a recent approach for uniformly…

In Random Matrix Theory the local correlations of the Laguerre and Jacobi Unitary Ensemble in the hard edge scaling limit can be described in terms of the Bessel kernel (containing a parameter $\alpha$). In particular, the so-called hard…

Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive…

I present the QCD short distance coefficient $\eta_3$ of the $\Delta S=2$ hamiltonian in the \emph{next-to-leading order} (NLO) of renormalization group improved perturbation theory. Since now all QCD-factors $\eta_1$, $\eta_2$ and $\eta_3$…