Related papers: Statistical Physics of Coding for the Integers
We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
The outcomes of projective measurements on a quantum many-body system in a chosen basis are inherently probabilistic. The Shannon entropy of this probability distribution (the "diagonal entropy") often reveals universal features, such as…
We consider the remote vector source coding problem in which a vector Gaussian source is to be estimated from noisy linear measurements. For this problem, we derive the performance of the compress-and-estimate (CE) coding scheme and compare…
The Hagedorn regime of string theory is usually understood as an equilibrium limiting phenomenon: the exponential growth of the density of states makes the canonical partition function singular at the Hagedorn temperature, while in the…
A novel coding strategy for block-based compressive sens-ing named spatially directional predictive coding (SDPC) is proposed, which efficiently utilizes the intrinsic spatial cor-relation of natural images. At the encoder, for each block…
We study the channel output distribution induced by a rate-$R$ random code via statistical physics. The partition function is $Z_n(\beta|\mathcal{C}) = \sum_{y^n}[P_{Y^n|\mathcal{C}}(y^n)]^\beta$, where $\mathcal{C}$ is the code and $\beta…
We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…
The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as $A$ and $B$, is computed analytically using a Coulomb gas method. It is shown that this probability, for large…
We introduce a new code for computing time-dependent continuum radiative transfer and non-equilibrium ionization states in static density fields with periodic boundaries. Our code solves the moments of the radiative transfer equation,…
In statistical mechanics one packages the possible energies of a system into a partition function. In number theory, and elsewhere in mathematics, one packages the spectrum of a phenomenon, say the prime numbers, into a $\zeta$-function or…
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter,…
Number theory is considered, by proposing quantum mechanical models and string-like models at zero and finite temperatures, where the factorization of number into prime numbers is viewed as the decay of particle into elementary particles…
The division by N! in the expression of statistical entropy is usually justified to students by the statement that classical particles should be counted as indistinguishable. Sometimes, quantum indistinguishability is invoked to explain it.…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
A stable non ideal Bose system whose energy operator includes a perturbations depending on the square root of the number operator associated to the zero mode energy is analyzed, demonstrating that, in presence or absence of a gap in the one…
Recent results on effects of Bose-Einstein symmetrization in a system of independently produced particles are interpreted in terms of statistical physics. For a large class of distributions, the effective sizes of the system in momentum and…
This paper provides a probabilist point of view about some results in analytic number theory. The main tool is the family of Zeta laws, which is a consolation for the non-existence of an uniform law on the set of integers. We prove the…
We introduce a high-dimensional quantum encoding based on coherent mode-dependent single-photon subtraction from multimode squeezed states. This encoding can be seen as a generalization to the case of non-zero squeezing of the standard…
We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat…