Entropy of Partitions on Quantum Logic

Partition and entropy of partitions in quantum logic are introduced and their properties are investigated. The results are generalized to the general case of T-norm and T-conorm.     

Conditional Entropy of Partitions on Quantum Logic

A construction of conditional entropy of partitions on quantum logic is given, and the properties of conditional entropy are investigated.     

Conditional Entropy of Partitions on Quantum Logic

A construction of conditional entropy of partitions on quantum logic is given, and the properties of conditional entropy are investigated.     

Generalized Conditional Entropies of Partitions on Quantum Logic

For partitions on quantum logic, the Rényi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.     

Generalized Conditional Entropies of Partitions on Quantum Logic

For partitions on quantum logic, the R閚yi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.     

The Number of Large Graphs with a Positive Density of Triangles

We give upper and lower bounds on the number of graphs of fixed degree which have a positive density of triangles. In particular, we show that there are very few such graphs, when compared to the number of graphs without this restriction. We also show that in this case the triangles seem to cluster even at low density.     

Transport Efficiency of Continuous-Time Quantum Walks on Graphs

Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on the initial state and specific features of the graph under investigation. In this paper, we address the role of graph topology, and investigate the transport properties of graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence, and assume a single trap vertex that is accountable for the loss processes. In particular, for each graph, we analytically determine the subspace of states having maximum transport efficiency. Our results provide a set of benchmarks for environment-assisted quantum transport, and suggest that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific correlations between transport efficiency and connectivity for certain graphs, but, in general, they are uncorrelated.     

The Neutron as a Quantum Object

Neutron interference experiments elucidate various properties of matter waves and permit a novel kind of wave function tomography.     

The Entropy of Partitions on MV-Algebras

Partitions of MV-algebras are studied. Using the notion of a state (as a probabilisticmeasure) on MV-algebras, we introduce the entropy of partitions. We show asuitable method for the refinement of partitions and the subadditivity of theentropy with respect to this refinement.     

量子阱数量变化对InGaN/AlGaN LED的影响

采用软件理论分析的方法分析了InGaN/AlGaN量子阱数量变化对发光二极管内量子效率、电子空穴浓度分布、载流子溢出产生的影响。分析结果表明:量子阱的个数不是越多越好,LED的光学性质和量子阱的个数并不成线性关系。量子阱个数太少时,电流溢出现象较明显;而当量子阱个数太多时,极化现象明显,且会造成材料浪费。因此应根据工作电流选择合适的量子阱个数。     

Spectra of Schrödinger Operators on Equilateral Quantum Graphs

We consider magnetic Schrödinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator. In particular, it is shown that the spectrum on the quantum graph is the preimage of the combinatorial spectrum under a certain entire function. Using this Correspondence we show that the number of gaps in the spectrum of the Schrödinger operators admits an estimate from below in terms of the Hill operator independently of the graph structure.     

Critical Value of the Quantum Ising Model on Star-Like Graphs

We present a rigorous determination of the critical value of the ground-state quantum Ising model in a transverse field, on a class of planar graphs which we call star-like. These include the junction of several copies of ℤ at a single point. Our approach is to use the graphical, or fk-, representation of the model, and the probabilistic and geometric tools associated with it. This research was carried out during the author’s Ph.D. studentship at the University of Cambridge, UK, and the Royal Institute of Technology (KTH), Sweden. The author gratefully acknowledges funding from KTH during this period. The author would also like to thank Riddarhuset, Stockholm, for generous support during his studies.     

Stability of a Model of Relativistic Quantum Electrodynamics

The relativistic “no pair” model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A– in the Coulomb gauge. There are no positrons because the electron wave functions are constrained to lie in the positive spectral subspace of some Dirac operator, D, but the model is defined for any number, N, of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, K, of fixed nuclei with charges ≤Z. If the fields are not quantized but are classical, it was shown earlier that such a model is always unstable (the ground state energy E=−∞) if one uses the customary D(0) to define the electron space, but is stable (E > − const.(N+K)) if one uses D(A) itself (provided the fine structure constant α and Z are not too large). This result is extended to quantized fields here, and stability is proved for α= 1/137 and Z≤ 42. This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons. Received: 8 September 2001 / Accepted: 18 March 2002     

Space as a Low-Temperature Regime of Graphs

I define a statistical model of graphs in which 2-dimensional spaces arise at low temperature. The configurations are given by graphs with a fixed number of edges and the Hamiltonian is a simple, local function of the graphs. Simulations show that there is a transition between a low-temperature regime in which the graphs form triangulations of 2-dimensional surfaces and a high-temperature regime, where the surfaces disappear. I use data for the specific heat and other observables to discuss whether this is a phase transition. The surface states are analyzed with regard to topology and defects.     

The Roles of a Quantum Channel on a Quantum State

When a quantum state undergoes a quantum channel, the state will be inevitably influenced. In general, the fidelity of the state is reduced, so is the entanglement if the subsystems go through the channel. However, the influence on the coherence of the state is quite different. Here we present some state-independent quantities to describe to what degree the fidelity, the entanglement and the coherence of the state are influenced. As applications, we consider some quantum channels on a qubit and find that the infidelity ability monotonically depends on the decay rate, but in usual the decoherence ability is not the case and strongly depends on the channel.     

Stability of an Electron-Hole Liquid in a Quantum Wire

Russian Physics Journal -     

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on compficated graphs. Using this method, we calculate the probability of Continuous-time classical and quantum random walks on many of finite direct product Cayley graphs （complete cycle, complete Kn, charter and n-cube）. Also, we inquire that the classical state the stationary uniform distribution is reached as t→∞ but for quantum state is not always satisfied.