[en] Entanglement catalysis is a phenomenon that usually enhances the conversion probability in the transformation of entangled states by the temporary involvement of another entangled state (so-called catalyst), where after the process is completed the catalyst is returned to the same state. For some pairs of bipartite pure entangled states, catalysis enables a transformation with unit probability of success, in which case the respective Schmidt coefficients of the states are said to satisfy the trumping relation, a mathematical relation which is an extension of the majorization relation. This paper provides all necessary and sufficient conditions for the trumping and two other associated relations. Using these conditions, the least upper bound of conversion probabilities using catalysis is also obtained. Moreover, best conversion ratios achievable with catalysis are found for transformations involving many copies of states

[en] A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann–Feynman theorem produces the final statement of the virial theorem. (paper)

[en] The linear thermal conductance of a quantum point contact displays a half-plateau structure, almost flat regions appearing close to half-integer multiples of the conductance quantum. This structure is investigated for the saddle-potential model; its behaviour as a function of contact parameters is also investigated. Half plateaus appear when the thermal energy is less than the subband separation and greater than the energy scale over which the transmission probability for a subband changes. The effect arises from the presence of a current node in the energy-resolved heat current, an energy at which the current is zero. When the transmission steps cross the current node as the gate voltage is varied, the heat conductance remains constant, creating the half plateaus, and this happens only for a certain temperature range. It is found that with increasing temperature the half plateaus become wider and flatter, which makes them more pronounced. It is also found that no half plateaus are present at the first step for any parameter values, and this is tied to the effect that the current node is pushed above the first step by the strong Seebeck potential

[en] The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.

[en] Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operations are also deterministic transformations by themselves. Finally, it is found that there are disjoint classes of states, all of which can be identified by a single real parameter, which remain invariant under deterministic transformations.

[en] Any quantum operation applied on a physical system is performed as a unitary transformation on a larger extended system. If the extension used is a heat bath in thermal equilibrium, the concomitant change in the state of the bath necessarily implies a heat exchange with it. The dependence of the average heat transferred to the bath on the initial state of the system can then be found from the expectation value of a Hermitian operator, which is named as the heat transfer operator (HTO). The purpose of this paper is to investigate the relation between the HTOs and the associated quantum operations. Since any given quantum operation on a system can be realized by different baths and unitaries, many different HTOs are possible for each quantum operation. On the other hand, there are also strong restrictions on the HTOs which arise from the unitarity of the transformations. The most important of these is the Landauer erasure principle. This paper is concerned with the question of finding a complete set of restrictions on the HTOs that are associated with a given quantum operation. An answer to this question has been found only for a subset of quantum operations. For erasure operations, these characterizations are equivalent to the generalized Landauer erasure principle. For the case of generic quantum operations, however, it appears that the HTOs obey further restrictions which cannot be obtained from the entropic restrictions of the generalized Landauer erasure principle.

[en] A phenomenological Ginzburg-Landau theory is applied to the normal phase of one-dimensional charge-density-wave systems with a finite concentration of impurities. It is found that the interaction between the impurities and the highly polarizable electron gas leads to a strong and oscillatory impurity-impurity interaction, which in turn leads to ordered impurity arrangements and to sizable periodic lattice distortions. The effect is very strongly dependent on the charge of the impurities, their concentration, and their (interstitial) location in the lattice unit cell. All these factors modify drastically the periodicity associated with the lattice distortion. The theory explains satisfactorily the changing modulation recently observed by atomic-force microscopy in the normal (room-temperature) phase of NbSe₃ with a variety of impurities

[en] A phenomenological Ginzburg-Landau theory of charge-density waves is presented. It yields, in the absence of pinning impurities, a manifold of stable (equal-energy) states that are independent of the phase of the wave. The pinning of these waves by impurities (both weak and strong pinning) is examined in detail and spectra for various impurity distributions are analyzed in detail. Strong dependence on the wave phase, change in harmonic content, and phase shifts are common features, in addition to the appearance of a continuous background. There is also a plethora of metastable states, many of which have energies close to the ground state. Comparison between the proposed theory and experiment in NbSe₃ is satisfactory

[en] The question of gauge covariance in the non-Abelian gauge-field formulation of two space-dimensional systems with spin–orbit coupling relevant to spintronics is investigated. Although these are generally gauge-fixed models, it is found that for the class of gauge fields that are spacetime independent and satisfy a U(1) algebra, thus having a vanishing field strength, there is a residual gauge freedom in the Hamiltonian. The gauge transformations assume the form of a space-dependent rotation of the transformed wavefunctions with rotation angles and axes determined by the specific form of the gauge field, i.e. the spin–orbit coupling. The fields can be gauged away, reducing the Hamiltonian to one which is isospectral to the free-particle Hamiltonian, and giving rise to the phenomenon of persistent spin helix reported first by Bernevig et al (2006 Phys. Rev. Lett. 97 236601). The investigation of the global gauge transformations leads to the derivation of a continuity equation where the component of the spin density along given directions, again fixed by the specific form of the gauge field, is conserved. (paper)