Complexity in strongly correlated electron systems is analyzed by considering decoherence process between the localized state, |L> and the itinerant state, |I>. The coherent superposition state of a|I> + b|L> decoheres to the pointer states in the proximity of both extremes of the correlation where the symmetry-breaking ground states of the charge pairing emerge. For maximizing the entropy of the system, the superconducting pairing and the spin density wave coexist within the uncertainty principle, which invokes the metastable states as like pseudogap phase and electronic inhomogenity.
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this concept to the many-particle scenario and determine the influence of the exchange symmetry. Moreover, we characterize the relation of multiparticle coherence to the entanglement of the compound quantum system. To support our general treatment with examples, we consider the quantum correlations of a collection of qudits. The impact of local and global quantum superpositions on the different forms of quantum correlations is discussed. For differently correlated states in the bipartite and multipartite scenarios, we provide a comprehensive characterization of the various forms and origins of quantum correlations.
Entanglement can be understood as an extraordinary degree of correlation between states of quantum systems – a correlation that cannot be given an explanation in terms of something like a common cause. Entanglement can occur between two or more quantum systems, and the most interesting case is when these correlations occur between systems that are space-like separated, meaning that changes made to one system are immediately correlated with changes in a distant system even though there is no time for a signal to travel between them. In this case one says that quantum entanglement leads to non-local correlations, or non-locality. More precisely, entanglement can be defined in the following way. Consider two particles, A and B, whose (pure) states can be represented by the state vectors ψA and ψB. Instead of representing the state of each particle individually, one can represent the composite two-particle system by another wavefunction, Ψ AB. If the two particles are unentangled , then the composite state is just the tensor product of the states of the components: Ψ AB = ψ A ⊗ ψ B; the state is then said to be factorable (or separable). If the particles are entangled, however, then the state of the composite system cannot be written as such a product of a definite state for A and a definite state for B. This is how an entangled state is defined for pure states: a state is entangled if and only if it cannot be factored: Ψ AB ≠ ψ A ⊗ ψ B.
In the present work, we present an investigation on quantum entanglement of the two-electron helium atom immersed in weakly coupled Debye plasmas, modeled by the Debye-Hückel, or screened Coulomb, potential to mimic the interaction between two charged particles inside the plasma. Quantum entanglement is related to correlation effects in a multi-particle system. In a bipartite system, a measurement made on one of the two entangled particles affects the outcome of the other particle, even if such two particles are far apart. Employing wave functions constructed with configuration interaction B-spline basis, we have quantified von Neumann entropy and linear entropy for a series of He 1,3Se and 1,3Po states in plasma-embedded helium atom.
The change-over from phase- to amplitude-fluctuation-driven superconductivity is examined for a composite system of free electrons (fermions with concentration
nF) and localized electron pairs (hard-core bosons with concentration
nB) as a function of doping---changing the total concentration of charge carriers
(ntot=nF+2nB). The coupling together of these two subsystems via a charge exchange term induces electron pairing and ultimately superconductivity in the fermionic subsystem. The difference in statistics of the two species of charge carriers has important consequences on the doping mechanism, showing an onset temperature
T∗ of incoherent electron pairing in the fermionic subsystem (manifest in form of a pseudogap), which steadily decreases with decreasing
ntot. Below
T∗ this electron pairing leads, in the normal phase, to electron-pair resonant states (Cooperons) with quasiparticle features which strongly depend on
ntot. For high concentrations, where ${n}_{B}\ensuremath{\simeq}0.5,$ correlation effects between the hard-core bosons lead to itinerant Cooperons having a heavy mass
mp, but are long lived. Upon reducing the concentration of charge carriers and consequently
nB, the mass as well as the lifetime of those Cooperons is considerably reduced. As a result, for high values of
nB, a superconducting state below
T∗ sets in at a
Tc, being controlled by the phase stiffness ${D}_{\ensuremath{\varphi}}={\ensuremath{\Elzxh}}^{2}{n}_{p}{/m}_{p}$ of those Cooperons, where
np denotes their density. Upon reducing
ntot, the phase stiffness steadily increases, and eventually exceeds the pairing energy
kBT∗. There, the Cooperons loose their well defined itinerant quasi-particle features and superconductivity gets controlled by amplitude fluctuations. The resulting phase diagram with doping is reminiscent of that of the phase fluctuation scenario for high-
Tc superconductivity, except that in our scenario the determinant factors are the mass and the lifetime of the Cooperons rather than their density.
Quantum entanglement, the most remarkable feature of quantum physics, is recognized as a resource for quantum information processing. The quest for quantum-computing devices has also produced great interest in entanglement formation in solid-state systems involving quantum effects. Indeed, the functionality of an increasing number of nanodevices is influenced by quantum correlations. In this work a theoretical approach developed in recent years to study the entanglement of fermions interacting via a Coulomb potential is presented, together with a number of applications to specific situations of physical interest in the field of charge transport in semiconductor nanostructures.