Quantum Statistical Model Research Articles

Derivation of quantum Chernoff metric with perturbation expansion method

We investigate a measure of distinguishability defined by the quantum Chernoff bound, which naturally induces the quantum Chernoff metric over a manifold of quantum states. Based on a quantum statistical model, we alternatively derive this metric by means of perturbation expansion. Moreover, we show that the quantum Chernoff metric coincides with the infinitesimal form of the quantum Hellinger distance, and reduces to the variant version of the quantum Fisher information for the single-parameter case. We also give the exact form of the quantum Chernoff metric for a qubit system containing a single parameter.

Ramp compression of diamond to five terapascals.

The recent discovery of more than a thousand planets outside our Solar System, together with the significant push to achieve inertially confined fusion in the laboratory, has prompted a renewed interest in how dense matter behaves at millions to billions of atmospheres of pressure. The theoretical description of such electron-degenerate matter has matured since the early quantum statistical model of Thomas and Fermi, and now suggests that new complexities can emerge at pressures where core electrons (not only valence electrons) influence the structure and bonding of matter. Recent developments in shock-free dynamic (ramp) compression now allow laboratory access to this dense matter regime. Here we describe ramp-compression measurements for diamond, achieving 3.7-fold compression at a peak pressure of 5 terapascals (equivalent to 50 million atmospheres). These equation-of-state data can now be compared to first-principles density functional calculations and theories long used to describe matter present in the interiors of giant planets, in stars, and in inertial-confinement fusion experiments. Our data also provide new constraints on mass-radius relationships for carbon-rich planets.

A note on the Landauer principle in quantum statistical mechanics

The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than kBT log 2. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system \documentclass[12pt]{minimal}\begin{document}${\cal S}$\end{document}S coupled to an infinitely extended thermal reservoir \documentclass[12pt]{minimal}\begin{document}${\cal R}$\end{document}R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system \documentclass[12pt]{minimal}\begin{document}${\cal S}+{\cal R}$\end{document}S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work [Reeb, D. and Wolf M. M., “(Im-)proving Landauer's principle,” preprint arXiv:1306.4352v2 (2013)] on the subject is discussed and compared.

Quantum Blackwell–Sherman–Stein Theorem and Related Results

We investigate the problem of comparing quantum statistical models in the general operator algebra framework in arbitrary dimension, thus generalizing results obtained so far in finite dimension, and for the full algebra of operators on a Hilbert space. In particular, the quantum Blackwell–Sherman–Stein theorem is obtained, and informational subordination of quantum information structures is characterized.

A quantum statistical model for graphene FETs on SiC

We present a quantum statistical model for nanoscale graphene field-effect transistors (FETs) on a SiC substrate. In the model, the scattering events as well as ballistic transport are taken into account. The channel charge and current are calculated with the Keldysh non-equilibrium Green's function technique. The model, which is meant for the design of the graphene FETs, is semianalytical, but it is easy to reduce the model to a simple fully analytical one, which then can be applied to the design of the integrated circuits made of graphene. It is shown that the neglect of the scattering would lead to too large values for the saturation current. The calculated transconductance and the on-off ratio for the saturation current are in agreement with the experimental results.

Density determinations in heavy ion collisions

The experimental determination of freeze-out temperatures and densities from the yields of light elements emitted in heavy ion collisions is discussed. Results from different experimental approaches are compared with those of model calculations carried out with and without the inclusion of medium effects. Medium effects become of relevance for baryon densities above $\approx 5 \times 10^{-4}$ fm$^{-3}$. A quantum statistical (QS) model incorporating medium effects is in good agreement with the experimentally derived results at higher densities. A densitometer based on calculated chemical equilibrium constants is proposed.

Quantum local asymptotic normality based on a new quantum likelihood ratio

We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.

Generating quantum-measurement probabilities from an optimality principle

An alternative formulation to the (generalized) Born rule is presented. It involves estimating an unknown model from a finite set of measurement operators on the state. An optimality principle is given that relates to achieving bounded solutions by regularizing the unknown parameters in the model. The objective function maximizes a lower bound on the quadratic Renyi classical entropy. The unknowns of the model in the primal are interpreted as transition witnesses. An interpretation of the Born rule in terms of fidelity is given with respect to transition witnesses for the pure state and the case of positive operator-valued measures (POVMs). The models for generating quantum-measurement probabilities apply to orthogonal projective measurements and POVM measurements, and to isolated and open systems with Kraus maps. A straightforward and constructive method is proposed for deriving the probability rule, which is based on Lagrange duality. An analogy is made with a kernel-based method for probability mass function estimation, for which similarities and differences are discussed. These combined insights from quantum mechanics, statistical modeling, and machine learning provide an alternative way of generating quantum-measurement probabilities.

Квантово-статистическая модель электронно-ионной системы сплавов Fe

Квантово-статистическая модель электронно-ионной системы сплавов Fe

KMS States and Conformal Measures

From a non-constant holomorphic map on a connected Riemann surface we construct an étale second countable locally compact Hausdorff groupoid whose associated groupoid C*-algebra admits a one-parameter group of automorphisms with the property that its KMS states correspond to conformal measures in the sense of Sullivan. In this way certain quadratic polynomials give rise to quantum statistical models with a phase transition arising from spontaneous symmetry breaking.

Nuclear matter symmetry energy at0.03⩽ρ/ρ0⩽0.2

Measurements of the density dependence of the free symmetry energy in low density clustered matter have been extended using the NIMROD multi-detector at Texas A&M University. Thermal coalescence models were employed to extract densities, $\rho$, and temperatures, $T$, for evolving systems formed in collisions of 47 $A$ MeV $^{40}$Ar + $^{112}$Sn,$^{124}$Sn and $^{64}$Zn + $^{112}$Sn, $^{124}$Sn. Densities of $0.03 \leq \rho/\rho_0 \leq 0.2$ and temperatures in the range 5 to 10 MeV have been sampled. The free symmetry energy coefficients are found to be in good agreement with values calculated using a quantum statistical model. Values of the corresponding symmetry energy coefficient are derived from the data using entropies derived from the model.

Noninformative prior in the quantum statistical model of pure states

In the present paper, we consider a suitable definition of a noninformative prior on the quantum statistical model of pure states. While the full pure-states model is invariant under unitary rotation and admits the Haar measure, restricted models, which we often see in quantum channel estimation and quantum process tomography, have less symmetry and no compelling rationale for any choice. We adopt a game-theoretic approach that is applicable to classical Bayesian statistics and yields a noninformative prior for a general class of probability distributions. We define the quantum detection game and show that there exist noninformative priors for a general class of a pure-states model. Theoretically, it gives one of the ways that we represent ignorance on the given quantum system with partial information. Practically, our method proposes a default distribution on the model in order to use the Bayesian technique in the quantum-state tomography with a small sample.

Establishment and Validation of Total Quantum Statistical Moment Similarity for Radix et Rhizoma Rhei Chromatographic Fingerprints

A new qualitative and quantitative analytical method for the interpretation of chromatographic fingerprints for Radix et Rhizoma Rhei was elucidated and established by using the original total quantum statistical moment similarity model (TQSMS) [1,2]. The TQSMS model consists of five main parameters: total quantum statistical moment similarity (ST), total mean variability (DT), total variable probability (PT) and total variable confident probability (1-β(á)), as well as total stable confident probability (β(1-á)). The TQSMS parameters of the chromatographic fingerprints for Radix et Rhizoma Rhei from different producing locations were obtained as ST 0.94±0.04, DT 0.07±0.05, PT 0.05±0.04, 1-β (á) 0.029±0.004 and β (1-á) 0.941±0.007, respectively. ST was higher than the confident critical value of 0.803. The results displayed the similarity of the chromatographic fingerprint for Radix et Rhizoma Rhei from different places and the TQSMS parameters might be considered as characteristics for the profile of chromatographic fingerprints [3].

Comparison of Quantum Statistical Models: Equivalent Conditions for Sufficiency

A family of probability distributions (i.e. a statistical model) is said to be sufficient for another, if there exists a transition matrix transforming the probability distributions in the former to the probability distributions in the latter. The Blackwell-Sherman-Stein (BSS) theorem provides necessary and sufficient conditions for one statistical model to be sufficient for another, by comparing their information values in statistical decision problems. In this paper we extend the BSS theorem to quantum statistical decision theory, where statistical models are replaced by families of density matrices defined on finite-dimensional Hilbert spaces, and transition matrices are replaced by completely positive, trace-preserving maps (i.e. coarse-grainings). The framework we propose is suitable for unifying results that previously were independent, like the BSS theorem for classical statistical models and its analogue for pairs of bipartite quantum states, recently proved by Shmaya. An important role in this paper is played by statistical morphisms, namely, affine maps whose definition generalizes that of coarse-grainings given by Petz and induces a corresponding criterion for statistical sufficiency that is weaker, and hence easier to be characterized, than Petz's.

Light clusters in nuclear matter: Excluded volume versus quantum many-body approaches

The formation of clusters in nuclear matter is investigated, which occurs e.g. in low energy heavy ion collisions or core-collapse supernovae. In astrophysical applications, the excluded volume concept is commonly used for the description of light clusters. Here we compare a phenomenological excluded volume approach to two quantum many-body models, the quantum statistical model and the generalized relativistic mean field model. All three models contain bound states of nuclei with mass number A <= 4. It is explored to which extent the complex medium effects can be mimicked by the simpler excluded volume model, regarding the chemical composition and thermodynamic variables. Furthermore, the role of heavy nuclei and excited states is investigated by use of the excluded volume model. At temperatures of a few MeV the excluded volume model gives a poor description of the medium effects on the light clusters, but there the composition is actually dominated by heavy nuclei. At larger temperatures there is a rather good agreement, whereas some smaller differences and model dependencies remain.

Generalized Superconducting Gap in an Anisotropic Boson–Fermion Mixture with a Uniform Coulomb Field

A boson–fermion (BF) quantum-statistical binary gas mixture model of high- T c superconductors (HTSCs) recently introduced consists of resonant bosonic Cooper electron pairs (CPs) in chemical and thermal equilibrium with single unpaired electrons. Here, this model is refined and extended to include: i) the anisotropy of the original BF vertex interaction causing boson formation/disintegration and ii) momentum-independent Coulomb repulsions between electron charge carriers. It is shown that pair breakings due to Coulomb repulsion depend on the separation between boson and fermion spectra. Specifically, as such a separation shrinks, the pair-breaking ability of the Coulomb interaction weakens and disappears altogether at the Bose–Einstein condensation (BEC) T c , i.e., at the temperature at which a complete softening of bosons occurs due to boson self-energy renormalization. Simultaneous inclusion of both effects produces “islands” in momentum space of incoherent CPs above the Fermi sea as temperature is lowered. These islands grow upon further cooling and merge together just before T c is reached. The BF model thusly extended now predicts a pseudogap phase in 2D HTSCs with lines of points on the Fermi surface along which the pseudogap vanishes, hence explaining the origin of the temperature-dependent “Fermi arcs” observed in experiments.

Quantum and quasiclassical state-to-state dynamics of the NH + H reaction: Competition between abstraction and exchange channels

Quantum and quasiclassical state-to-state dynamics for the NH + H' reaction at high collision energies up to 1.6 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction (NH + H' → N + HH') and thermoneutral exchange (NH + H' → H + NH') channels were investigated from the same set of wave packets using an efficient coordinate transformation method. It is found that the abstraction represents a minor reaction channel in the energy range studied, primarily due to endothermicity. The cross section for the abstraction reaction increases monotonically with the collision energy, while that for the exchange reaction is relatively energy insensitive. As a result, the thermal rate constant for the abstraction reaction follows the Arrhenius law, where that for the exchange reaction is nearly temperature independent. Finally, it is shown that the quantum mechanical results can be reasonably reproduced by the Gaussian-binning quasiclassical trajectory method and to a lesser extent by a quantum statistical model.

A compact quantum statistical model for the ballistic nanoscale MOSFETs

AbstractWe develop an analytical quantum statistical model for nanoscale metal‐oxide‐semiconductor field‐effect transistors (MOSFETs). The model describes transport both in the scattering‐limited and ballistic regimes. The expression for the channel current is derived with the Keldysh nonequilibrium Green's function technique. The obtained quantum statistical current expression reduces to the semiclassical one in the absence of scattering. The model indicates that in nanoscale devices the scattering processes become dependent on the bias voltages. The calculated results for the I–V characteristics are in good agreement with the experimental results in the case of a 70 nm MOSFET. The model includes a minimal number of fitting parameters and it can be used in the design of ultra large‐scale integrated circuits.

$\mathcal{PT}$ Symmetry in Statistical Mechanics and the Sign Problem

Generalized \(\mathcal{PT}\) symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state energy of a non-Hermitian, but generalized \(\mathcal{PT}\)-symmetric Hamiltonian. There is a corresponding class of \(\mathcal{PT}\)-symmetric classical statistical mechanics models with non-Hermitian transfer matrices. We discuss a class of Z(N) spin models with explicit \(\mathcal{PT}\) symmetry and also the ANNNI model, which has a hidden \(\mathcal{PT}\) symmetry. For both quantum and classical models, the class of models with generalized \(\mathcal{PT}\) symmetry is precisely the class where the complex weight problem can be reduced to real weights, i.e., a sign problem. The spatial two-point functions of such models can exhibit three different behaviors: exponential decay, oscillatory decay, and periodic behavior. The latter two regions are associated with \(\mathcal{PT}\) symmetry breaking, where a Hamiltonian or transfer matrix has complex conjugate pairs of eigenvalues. The transition to a spatially modulated phase is associated with \(\mathcal{PT}\) symmetry breaking of the ground state, and is generically a first-order transition. In the region where \(\mathcal{PT}\) symmetry is unbroken, the sign problem can always be solved in principle using the equivalence to a Hermitian theory in this region. The ANNNI model provides an example of a model with \(\mathcal{PT}\) symmetry which can be simulated for all parameter values, including cases where \(\mathcal{PT}\) symmetry is broken.

GENERALIZED SUPERCONDUCTING GAP IN A BOSON-FERMION MODEL

A quantum-statistical binary gas mixture model consisting of positive-energy resonant bosonic Cooper electron pairs in chemical and thermal equilibrium with single unpaired electrons yields, via two-time retarded Green functions, an analytic expression for a dimensionless coupling λ- and temperature T-dependent generalized energy gap Eg(λ, T) in the single-electron spectrum. The new gap gives a reasonable description of overdoped Bi2Sr2CuO6+δ(Bi2201).