188 research outputs found
Mott-Hubbard transition in infinite dimensions
We analyze the unanalytical structure of metal-insulator transition (MIT) in
infinite dimensions. By introducing a simple transformation into the dynamical
mean-field equation of Hubbard model, a multiple-valued structure in Green's
function and other thermodynamical quantities with respect to the interaction
strength are found at low temperatures. A unified description of stable,
metastable and unstable phases is obtained in the regime
, and the Maxwell construction is performed to evaluate
the MIT line . We show how the first-order MIT at
for evolves into second-order one at for . The phase
diagram near MIT is presented.Comment: 5 pages with 3 figures, text and figures revise
Integrabilities of the Model with Impurities
The hamiltonian with magnetic impurities coupled to the strongly correlated
electron system is constructed from model. And it is diagonalized exactly
by using the Bethe ansatz method. Our boundary matrices depend on the spins of
the electrons. The Kondo problem in this system is discussed in details. The
integral equations are derived with complex rapidities which describe the bound
states in the system. The finite-size corrections for the ground-state energies
are obtained.Comment: 24 pages, Revtex, To be published in J. Phys.
Periodic Instanton and Phase Transition in Quantum Tunneling of Spin Systems
The quantum-classical transitions of the escape rates in a uniaxial spin
model relevant to the molecular magnet MnAc and a biaxial anisotropic
ferromagnetic particle are investigated by applying the periodic instanton
method. The effective free energies are expanded around the top of the
potential barrier in analogy to Landau theory of phase transitions. We show
that the first-order transitions occur below the critical external magnetic
field for the uniaxial spin model and beyond the critical
anisotropy constant ratio for the biaxial ferromagnetic grains,
which are in good agreement with earlier works.Comment: 14 pages, revtex, 5 postscript figure
Enhancement of pair correlation in a one-dimensional hybridization model
We propose an integrable model of one-dimensional (1D) interacting electrons
coupled with the local orbitals arrayed periodically in the chain. Since the
local orbitals are introduced in a way that double occupation is forbidden, the
model keeps the main feature of the periodic Anderson model with an interacting
host. For the attractive interaction, it is found that the local orbitals
enhance the effective mass of the Cooper-pair-like singlets and also the pair
correlation in the ground state. However, the persistent current is depressed
in this case. For the repulsive interaction case, the Hamiltonian is
non-Hermitian but allows Cooper pair solutions with small momenta, which are
induced by the hybridization between the extended state and the local orbitals.Comment: 11 page revtex, no figur
Unitarizable Representations of the Deformed Para-Bose Superalgebra Uq[osp(1/2)] at Roots of 1
The unitarizable irreps of the deformed para-Bose superalgebra , which
is isomorphic to , are classified at being root of 1. New
finite-dimensional irreps of are found. Explicit expressions
for the matrix elements are written down.Comment: 19 pages, PlainTe
Exact Results for a Kondo Problem in One Dimensional t-J Model
We propose an integrable Kondo problem in a one-dimensional (1D) model.
With the open boundary condition of the wave functions at the impurity sites,
the model can be exactly solved via Bethe ansatz for a class of
(Kondo coupling constants) and (impurity potentials) parametrized by
a single parameter . The integrable value of runs from negative
infinity to positive infinity, which allows us to study both the ferromagnetic
Kondo problem and antiferromagnetic Kondo problem in a strongly correlated
electron system. Generally, there is a residual entropy for the ground state,
which indicates a typical non-Fermi liquid behavior.Comment: 5 pages Revtex, no figure
Two Magnetic Impurities with Arbitrary Spins in Open Boundary t-J Model
From the open boundary t-J model, an impurity model is constructed in which
magnetic impurities of arbitrary spins are coupled to the edges of the strongly
correlated electron system. The boundary R matrices are given explicitly. The
interaction parameters between magnetic impurities and electrons are related to
the potentials of the impurities to preserve the integrability of the system.
The Hamiltonian of the impurity model is diagonalized exactly. The integral
equations of the ground state are derived and the ground state properties are
discussed in details. We discuss also the string solutions of the Bethe ansatz
equations, which describe the bound states of the charges and spins. By
minimizing the thermodynamic potential we get the thermodynamic Bethe ansatz
equations. The finite size correction of the free energy contributed by the
magnetic impurities is obtained explicitly. The properties of the system at
some special limits are discussed and the boundary bound states are obtained.Comment: 18 pages, Revte
Exact Boundary Critical Exponents and Tunneling Effect in Integrable Models for Quantum Wires
Using the principles of the conformal quantum field theory and the finite
size corrections of the energy of the ground and various excited states, we
calculate the boundary critical exponents of single- and multicomponent Bethe
ansatz soluble models. The boundary critical exponents are given in terms of
the dressed charge matrix which has the same form as that of systems with
periodic boundary conditions and is uniquely determined by the Bethe ansatz
equations. A Luttinger liquid with open boundaries is the effective low-energy
theory of these models. As applications of the theory, the Friedel oscillations
due to the boundaries and the tunneling conductance through a barrier are also
calculated. The tunneling conductance is determined by a nonuniversal boundary
exponent which governs its power law dependence on temperature and frequency.Comment: REVTEX, submitted to PR
Cancer Biomarker Discovery: The Entropic Hallmark
Background: It is a commonly accepted belief that cancer cells modify their transcriptional state during the progression of the disease. We propose that the progression of cancer cells towards malignant phenotypes can be efficiently tracked using high-throughput technologies that follow the gradual changes observed in the gene expression profiles by employing Shannon's mathematical theory of communication. Methods based on Information Theory can then quantify the divergence of cancer cells' transcriptional profiles from those of normally appearing cells of the originating tissues. The relevance of the proposed methods can be evaluated using microarray datasets available in the public domain but the method is in principle applicable to other high-throughput methods. Methodology/Principal Findings: Using melanoma and prostate cancer datasets we illustrate how it is possible to employ Shannon Entropy and the Jensen-Shannon divergence to trace the transcriptional changes progression of the disease. We establish how the variations of these two measures correlate with established biomarkers of cancer progression. The Information Theory measures allow us to identify novel biomarkers for both progressive and relatively more sudden transcriptional changes leading to malignant phenotypes. At the same time, the methodology was able to validate a large number of genes and processes that seem to be implicated in the progression of melanoma and prostate cancer. Conclusions/Significance: We thus present a quantitative guiding rule, a new unifying hallmark of cancer: the cancer cell's transcriptome changes lead to measurable observed transitions of Normalized Shannon Entropy values (as measured by high-throughput technologies). At the same time, tumor cells increment their divergence from the normal tissue profile increasing their disorder via creation of states that we might not directly measure. This unifying hallmark allows, via the the Jensen-Shannon divergence, to identify the arrow of time of the processes from the gene expression profiles, and helps to map the phenotypical and molecular hallmarks of specific cancer subtypes. The deep mathematical basis of the approach allows us to suggest that this principle is, hopefully, of general applicability for other diseases
Pan-cancer analysis of whole genomes
Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe
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