Related papers: Second Quantization and the Spectral Action
This paper considers the problem of data compression for dependent quantum systems. It is the second in a series under the same title. As in the previous paper, we are interested in Lempel--Ziv encoding for quantum Gibbs ensembles. Here, we…
We re-interprete the microcanonical conditions in the quantum domain as constraints for the interaction of the "gas-subsystem" under consideration and its environment ("container"). The time-average of a purity-measure is found to equal the…
We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the $\nu = 1/2$ state using the non-equilibrium Green's function technique. The lowest order perturbative correction to the self-energy due to the strong gauge…
In this work, we put forward the theoretical foundation toward thermodynamics of quantum impurity systems measurable in experiments. The theoretical developments involve the identifications on two types of thermodynamic entanglement…
We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral…
Entropy and free energy are central concepts in both statistical physics and information theory, with quantum and classical facets. In mathematics these concepts appear quite often in different contexts (dynamical systems, probability…
For a given quantum state $\rho$ and two quantum operations $\Phi$ and $\Psi$, the information encoded in the quantum state $\rho$ is quantified by its von Neumann entropy $\S(\rho)$. By the famous Choi-Jamio{\l}kowski isomorphism, the…
We show how (a slight modification of) the noncommutative geometry bosonic spectral action can be obtained by the cancelation of the scale anomaly of the fermionic action. In this sense the standard model coupled with gravity is induced by…
We derive several formulae for the spectra of the second quantization operators in abstract fermionic Fock spaces.
Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of…
A new class of quantum channels called Grassmann channels is introduced and their classical and quantum capacity is calculated. The channel class appears in a study of the two-mode squeezing operator constructed from operators satisfying…
Von Neumann entropy rate for open quantum systems is, in general, written in terms of entropy production and entropy flow rates, encompassing the second law of thermodynamics. When the open-quantum-system evolution corresponds to a quantum…
We present the Schmidt decomposition for arbitrary wavefunctions of two indistinguishable bosons, extending the recent studies of entanglement or quantum correlations for two fermion systems [J. Schliemann et al., Phys. Rev. B {\bf 63},…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form…
Spectral functions do not fully describe quasielastic electron and neutrino scattering from nuclei because they only model the initial state. Final state interactions distort the shape of the differential cross section at the peak and…
We study the canonical quantization of the theory given by Chamseddine-Connes spectral action on a particular finite spectral triple with algebra $M_2(\Cset)\oplus\Cset$. We define a quantization of the natural distance associated with this…
Studying the typical entanglement entropy of a bipartite system when averaging over different ensembles of pure quantum states has been instrumental in different areas of physics, ranging from many-body quantum chaos to black hole…
We find a simpler formulation of the Green-Schwarz action, for which the Wess-Zumino term is the square of supersymmetric currents, like the rest of the action. On a random lattice it gives Feynman diagrams of a particle superfield theory.
The spectral action on noncommutative torus is obtained, using a Chamseddine--Connes formula via computations of zeta functions. The importance of a Diophantine condition is outlined. Several results on holomorphic continuation of series of…