We consider a toy model of pointer interacting with a 1/2-spin system, whose σx variable is measured by the environment, according to the prescription of decoherence theory. If the environment measuring the variable σx yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation. : 03.65.Ta, Decoherence theory was born in 1970 with the seminal work of Zeh [1] and grew up with the work of Zurek and others over the following decades. It is now regarded to be a theory so robust as to make Tegmark and Wheeler [2] claim that it renders obsolete the hypothesis of wave function collapses made by the founding fathers of quantum mechanics. The main purpose of this paper is to prove that this claim is correct only in the case when decoherence is caused by interactions compatible with ordinary statistical mechanics. If we move from the condition of exponential relaxation, which is the key property of ordinary statistical mechanics, to the condition of inverse power law relaxation, the statistical equivalence between wave-function collapses and decoherence is lost. To show this basic property, let us consider the following toy Hamiltonian PacswhereWe have a 1/2-spin system, characterized by the Pauli matrix Σ, called pointer, interacting with a 1/2-spin system, characterized by the Pauli matrix σ, and called system of interest. The system of interest undergoes an interaction with a bath, through a variable η, driven by the Hamiltonian H B . The density matrices of the pointer and of the system of interest are called ρ Σ and ρ σ , respectively. The former is obtained from a contraction over the degrees of freedom of the system of interest, and of its bath as well. The latter requires a contraction over the pointer degrees of freedom as well as on the bath of the system of interest. This bath is assumed to be much faster than the pointer and, as a consequence, the time evolution of σ x is virtually independent of the pointer dynamics.First of all, we show that in the special case where the correlation function of the fluctuation η is exponential, the two pictures, wave-function collapses and decoherence, yield the same statistical result. This supports the point of view of the advocates of decoherence. Then, we create a condition of anomalous statistical mechanics, by modulating the Hamiltonian H σ in such a way as to create a significant departure from ordinary exponential relaxation. In this case, we show that the two perspectives yield quite different results. In a sense, the decoherence theory is not contradicted, in so far as the pointer density matrix becomes diagonal in the basis set of the poin...
We study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization. Recently Latora and Baranger ͓Phys. Rev. Lett. 82, 520 ͑1999͔͒ found that there exist three entropy regimes, a transient regime of passage from dynamics to thermodynamics, a linear-in-time regime of entropy increase, that is, a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the nonextensive entropic indicator advocated by Tsallis ͓J. Stat. Phys. 52, 479 ͑1988͔͒ with a mobile entropic index q, and we find that the adoption of the ''magic'' value qϭQϭ1/2, compared to the traditional entropic index qϭ1, reduces the length of the transient regime and makes earlier the emergence of the Kolmogorov regime. We adopt a two-site model to explain these properties by means of an analytical treatment and we argue that Qϭ1/2 might be a typical signature of the occurrence of Anderson localization.
High contact resistance (R C ) between 3D metallic conductors and single-layer 2D semiconductors poses major challenges toward their integration in nanoscale electronic devices. While in experiments the large R C values can be partly due to defects, ab initio simulations suggest that, even in defect-free structures, the interaction between metal and semiconductor orbitals can induce gap states that pin the Fermi level in the semiconductor band gap, increase the Schottky barrier height (SBH), and thus degrade the contact resistance. In this paper, we investigate, by using an in-house-developed ab initio transport methodology that combines density functional theory and nonequilibrium Green's function (NEGF) transport calculations, the physical properties and electrical resistance of several options for ntype top metal contacts to monolayer MoS 2 , even in the presence of buffer layers, and for ptype contacts to monolayer WSe 2 . The delicate interplay between the SBH and tunneling barrier thickness is quantitatively analyzed, confirming the excellent properties of the Bi− MoS 2 system as an n-type ohmic contact. Moreover, simulation results supported by literature experiments suggest that the Au−WSe 2 system is a promising candidate for p-type ohmic contacts. Finally, our analysis also reveals that a small modulation of a few angstroms of the distance between the (semi)metal and the transition-metal dichalcogenide (TMD) leads to large variations of R C . This could help to explain the scattering of R C values experimentally reported in the literature because different metal deposition techniques can result in small changes of the metal-to-TMD distance besides affecting the density of possible defects.
We study the time evolution of a quantum system without classical counterpart, undergoing a process of entropy increase due to the environment influence. We show that if the environment-induced decoherence is interpreted in terms of wave-function collapses, a symbolic sequence can be generated. We prove that the Kolmogorov-Sinai entropy of this sequence coincides with rate of von Neumann entropy increase. 03.65.Sq,03.65.Bz According to Landau and Lifshitz [1,2] the foundation of the second law might lie in the processes of quantum measurement. This point of view, still under the form of a plausible conjecture, has been recently reformulated by Srivastava, Vitiello and Widom [3]. The authors of this interesting paper note that the von Neumann entropy, which is kept constant by the unitary transformation of quantum mechanics, increases as a consequence of the von Neumann projective measurement, and consequently as an effect of the occurrence of a quantum measurement. Their approach makes manifest the concept of heat and work during the measurement process. In summary, they prove that the von Neumann entropy expressed in terms of the von Neumann projected density matrix, as a consequence of quantum measurement, becomes indistinguishable from the physical entropy.The present letter focuses on a different aspect of the same fundamental issue. This has to do with the relation between physical entropy and Kolmogorov-Sinai (KS) entropy [4,5]. This latter form of entropy is actually a property of a classical trajectory [6,7]. The classical phase space is divided into cells, the cells are labelled with symbols, and a trajectory running in this phase space creates a symbolic sequence. Finally, using the KS entropy prescription this trajectory is assigned the value h KS that can be interpreted as a rate of entropy increase. In the recent past many papers have been devoted to the discussion of the possible connection between the KS entropy and the physical entropies [8][9][10][11][12][13][14][15][16][17]. Of special relevance for the discussion of this paper is the work of Latora and Baranger [17]. These authors study the time evolution of the physical entropy moving from an out of equilibrium initial condition and prove that three distinct time regimes exist: An initial regime of transition, an intermediate regime of linear increase and a saturation regime. The rate of entropy increase in the intermediate regime is proved by them to coincide with the KS entropy. Results of the same kind have been derived by Pattanyak [12] along lines that essentially adopt a perspective originally advocated by Zurek and Paz [8]. In a sense, the perspective of Zurek and Paz is the same as the perspective of Refs. [1][2][3] if we interpret the influence of the environment as a nature-made form of measurement [18][19][20]. However, the main limitation of all these papers is given by the fact that the adopted approach works only when the system studied has a classical counterpart. Thus, the corrrespondence between the original conjecture of L...
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