How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e. by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure.Comment: 22 page

Microbial responses to elevated temperature: Evaluating bentonite mineralogy and copper canister corrosion within the long-term stability of Deep Geological Repositories of nuclear waste

Deep Geological Repositories (DGRs) consist of radioactive waste contained in corrosion-resistant canisters, surrounded by compacted bentonite clay, and buried few hundred meters in a stable geological formation. The effects of bentonite microbial communities on the long-term stability of the repository should be assessed. This study explores the impact of harsh conditions (60 ºC, highly-compacted bentonite, low water activity), and acetate:lactate:sulfate addition, on the evolution of microbial communities, and their effect on the bentonite mineralogy, and corrosion of copper material under anoxic conditions. No bentonite illitization was observed in the treatments, confirming its mineralogical stability as an effective barrier for future DGR. Anoxic incubation at 60 ºC reduced the microbial diversity, with Pseudomonas as the dominant genus. Culture-dependent methods showed survival and viability at 60 ºC of moderate-thermophilic aerobic bacterial isolates (e.g., Aeribacillus). Despite the low presence of sulfate-reducing bacteria in the bentonite blocks, we proved their survival at 30 ºC but not at 60 ºC. Copper disk´s surface remained visually unaltered. However, in the acetate:lactate:sulfate-treated samples, sulfide/sulfate signals were detected, along with microbial-related compounds. These findings offer new insights into the impact of high temperatures (60ºC) on the biogeochemical processes at the compacted bentonite/Cu canister interface post-repository closure

Impact of compacted bentonite microbial community on the clay mineralogy and copper canister corrosion: a multidisciplinary approach in view of a safe Deep Geological Repository of nuclear wastes

The Deep Geological Repository (DGR) is the preferred option for the final disposal of high-level radioactive waste. Microorganisms could affect the safety of the DGR by altering the mineralogical properties of the compacted bentonite or inducing the corrosion of the metal canisters. In this work, the impact of physicochemical parameters (bentonite dry density, heat shock, electron donors/acceptors) on the microbial activity, stability of compacted bentonite and corrosion of copper (Cu) discs was investigated after one-year anoxic incubation at 30 ºC. No-illitization in the bentonite was detected confirming its structural stability over 1 year under the experimental conditions. The microbial diversity analysis based on 16S rRNA Next Generation Sequencing showed slight changes between the treatments with an increase of aerobic bacteria belonging to Micrococcaceae and Nocardioides in heat-shock tyndallized bentonites. The survival of sulfate-reducing bacteria (the main source of Cu anoxic corrosion) was demonstrated by the most probable number method. The detection of CuxS precipitates on the surface of Cu metal in the bentonite/Cu metal samples amended with acetate/lactate and sulfate, indicate an early stage of Cu corrosion. Altogether, the outputs of this study help to better understand the predominant biogeochemical processes at the bentonite/Cu canister interface upon DGR closure

Acquired Factor X Deficiency in Light Chain Amyloidosis: A Report of 2 Korean Cases

Amyloidosis is a heterogeneous group of diseases in which misfolding of extracellular proteins is the pathogenic factor. Light chain amyloidosis (AL) is the most common form of amyloidosis, and the causative proteins in AL are the immunoglobulin light chains produced by clonal plasma cells. Hemorrhagic events, ranging from mild subcutaneous hemorrhage to life-threatening bleeding, account for a significant proportion of morbidities and mortality in AL patients. Deficiency of factor X from deposition into amyloid fibrils has been reported to be the most common acquired factor deficiency in AL. We herein report 2 patients with acquired factor X deficiency in AL. A 55-yr-old woman with AL had a prolonged prothrombin time (PT) and an activated partial thromboplastin time (aPTT) of 2.51 International Normalized Ratio (INR) and 75.1 sec, respectively, which were corrected on mixing with normal plasma. Factor X activity was markedly decreased at 5%. The other patient was a 67-yr-old man with AL with a PT of 1.63 INR and an aPTT of 50.3 sec, which were corrected on mixing with normal plasma. Factor X activity was decreased at 17%. Neither of the patients had apparent hemorrhagic manifestations. Identification of acquired factor deficiency and timely coagulation tests are needed in the diagnostic workup and management in AL

Impact of compacted bentonite microbial community on the clay mineralogy and copper canister corrosion: a multidisciplinary approach in view of a safe Deep Geological Repository of nuclear wastes

Deep Geological Repository (DGR) is the preferred option for the final disposal of high-level radioactive waste. Microorganisms could affect the safety of the DGR by altering the mineralogical properties of the compacted bentonite or inducing the corrosion of the metal canisters. In this work, the impact of physicochemical parameters (bentonite dry density, heat shock, electron donors/acceptors) on the microbial activity, stability of compacted bentonite and corrosion of copper (Cu) discs was investigated after one-year anoxic incubation at 30 ºC. No-illitization in the bentonite was detected confirming its structural stability over 1 year under the experimental conditions. The microbial diversity analysis based on 16 S rRNA gene Next Generation Sequencing showed slight changes between the treatments with an increase of aerobic bacteria belonging to Micrococcaceae and Nocardioides in heat-shock tyndallized bentonites. The survival of sulfate-reducing bacteria (the main source of Cu anoxic corrosion) was demonstrated by the most probable number method. The detection of CuxS precipitates on the surface of Cu metal in the bentonite/Cu metal samples amended with acetate/lactate and sulfate, indicated an early stage of Cu corrosion. Overall, the outputs of this study help to better understand the predominant biogeochemical processes at the bentonite/Cu canister interface upon DGR closure

Torsion, topology and CPT anomaly in two-dimensional chiral U(1) gauge theory

We consider the CPT anomaly of two-dimensional chiral U(1) gauge theory on a torus with topologically nontrivial zweibeins corresponding to the presence of spacetime torsion. The resulting chiral determinant can be expressed in terms of the standard chiral determinant without torsion, but with modified spinor boundary conditions. This implies that the two-dimensional CPT anomaly can be moved from one spin structure to another by choosing appropriate zweibeins. Similar results apply to higher-dimensional chiral gauge theories.Comment: LaTeX with elsart.cls, 20 pages, v3: to appear in Nucl. Phys.

Convexity of momentum map, Morse index, and quantum entanglement

We analyze form the topological perspective the space of all SLOCC (Stochastic Local Operations with Classical Communication) classes of pure states for composite quantum systems. We do it for both distinguishable and indistinguishable particles. In general, the topology of this space is rather complicated as it is a non-Hausdorff space. Using geometric invariant theory (GIT) and momentum map geometry we propose a way to divide the space of all SLOCC classes into mathematically and physically meaningful families. Each family consists of possibly many `asymptotically' equivalent SLOCC classes. Moreover, each contains exactly one distinguished SLOCC class on which the total variance (a well defined measure of entanglement) of the state Var[v] attains maximum. We provide an algorithm for finding critical sets of Var[v], which makes use of the convexity of the momentum map and allows classification of such defined families of SLOCC classes. The number of families is in general infinite. We introduce an additional refinement into finitely many groups of families using the recent developments in the momentum map geometry known as Ness stratification. We also discuss how to define it equivalently using the convexity of the momentum map applied to SLOCC classes. Moreover, we note that the Morse index at the critical set of the total variance of state has an interpretation of number of non-SLOCC directions in which entanglement increases and calculate it for several exemplary systems. Finally, we introduce the SLOCC-invariant measure of entanglement as a square root of the total variance of state at the critical point and explain its geometric meaning.Comment: 37 pages, 2 figures, changes in the manuscript structur

Finite Temperature Schwinger Model with Chirality Breaking Boundary Conditions

The $N_f$-flavour Schwinger Model on a finite space $0\leq x^1\leq L$ and subject to bag-type boundary-conditions at $x^1=0$ und $x^1=L$ is solved at finite temperature $T=1/\beta$. The boundary conditions depend on a real parameter $\theta$ and break the axial flavour symmetry. We argue that this approach is more appropriate to study the broken phases than introducing small quark masses, since all calculations can be performed analytically. In the imaginary time formalism we determine the thermal correlators for the fermion-fields and the determinant of the Dirac-operator in arbitrary background gauge-fields. We show that the boundary conditions induce a CP-odd $\theta$-term in the effective action. The chiral condensate, and in particular its T- and L- dependence, is calculated for $N_f$ fermions. It is seen to depend on the order in which the two lengths $\beta=1/T$ and $L$ are sent to infinity.Comment: One reference added plus one corrected, final version as to be published in Annals of Physic