On the theory of electric dc-conductivity : linear and non-linear microscopic evolution and macroscopic behaviour

We consider the Schrodinger time evolution of charged particles subject to a static substrate potential and to a homogeneous, macroscopic electric field (a magnetic field may also be present). We investigate the microscopic velocities and the resulting macroscopic current. We show that the microscopic velocities are in general non-linear with respect to the electric field. One kind of non-linearity arises from the highly non-linear adiabatic evolution and (or) from an admixture of parts of it in so-called intermediate states, and the other kind from non-quadratic transition rates between adiabatic states. The resulting macroscopic dc-current may or may not be linear in the field. Three cases can be distinguished : (a) The microscopic non-linearities can be neglected. This is assumed to be the case in linear response theory (Kubo formalism, ...). We give arguments which make it plausible that often such an assumption is indeed justified, in particular for the current parallel to the field. (b) The microscopic non-linearitites lead to macroscopic non-linearities. An example is the onset of dissipation by increasing the electric field in the breakdown of the quantum Hall effect. (c) The macroscopic current is linear although the microscopic non-linearities constitute an essential part of it and cannot be neglected. We show that the Hall current of a quantized Hall plateau belongs to this case. This illustrates that macroscopic linearity does not necessarily result from microscopic linearity. In the second and third cases linear response theory is inadequate. We elucidate also some other problems related to linear response theory.Comment: 24 pages, 6 figures, some typing errors have been corrected. Remark : in eq. (1) of the printed article an obvious typing error remain

Approximate Deadline-Scheduling with Precedence Constraints

We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result is an O(log k)-approximation algorithm for instances with k distinct job deadlines

Gradual sub-lattice reduction and a new complexity for factoring polynomials

We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well

The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer

A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and `hidden' or `unknown' subgroups of Abelian groups. It is already known how to phrase the first four problems as the estimation of eigenvalues of certain unitary operators. Here we show how the solution to the more general Abelian `hidden subgroup problem' can also be described and analysed as such. We then point out how certain instances of these problems can be solved with only one control qubit, or `flying qubits', instead of entire registers of control qubits.Comment: 16 pages, 3 figures, LaTeX2e, to appear in Proceedings of the 1st NASA International Conference on Quantum Computing and Quantum Communication (Springer-Verlag

The community informatics of an aging society: a comparative case study of senior centers and public libraries

The information society is also an aging society. This means that as information technology becomes woven into the fabric of daily life, the median age of humanity continues to rise. The participation of this growing population of older adults in the information society is often seen in the popular press and even in scholarship as dependent on their ability to cope with their supposedly declining minds and declining bodies. This study reframes this phenomenon by studying older adults in the communities where they live. This dissertation asks to what extent and how does community-based information infrastructure support older adult digital literacy. Three theories shape this analysis: 1) information infrastructure as the co-creation of information systems and information users (Star & Ruhleder, 1996), 2) digital literacy as the integration of technology into our lives (Prior & Shipka, 2003), and 3) older adulthood as a socially shaped stage in the human lifecourse (Hutchison, 2014). Using the extended case method approach (Burawoy, 1998), these three theories are scrutinized in relation to the empirical reality I studied. Through this situated understanding (Suchman, 1987), this dissertation contributes to the development of these theories, which are used in multiple academic disciplines. This dissertation further contributes to the fields of community informatics and library & information science, both of which are only beginning to study aging in the information society. I study senior centers and public libraries, institutions that are ubiquitous in the United States of America, as community-based information infrastructure. This dissertation consists of a comparative case study of three public libraries and three senior centers in a particular Midwestern metropolitan area. I direct particular attention to 209 of the older adults who participate in technology support services at these six institutions. During a one-year period involving 267 field sessions I conducted participant observation with these older adults, as well as with staff. I also interviewed 54 of these older adults, and seven staff members. I finally reviewed documents produced in the past and in the present by and about the institutions. The overall finding from this investigation is that community-based information infrastructure is indeed supportive of older adult digital literacy. However, this support is not as robust as it could be. Particular findings include: 1) community-based information infrastructure emerges out of and evolves through individual and social struggle; 2) community-based information infrastructure is rooted in the lives of older adults; 3) ageism conditions both community-based information infrastructure and older adult digital literacy; and 4) older adults are determined and creative learners who with support integrate technology into the diverse rhythms of their lives. These lives can be best understood through a new concept articulated in this dissertation, the informatics lifecourse. This concept refers to how a person learns technology through the stages of his or her life. The informatics lifecourse is populated by countless informatics moments (Williams, 2012), instances of giving and receiving technology support. Breakdowns in the informatics lifecourse of the individual relate to breakdowns at the level of the community. This finding illustrates how individuals and communities are interdependent. By foregrounding the agency of older adults in the information infrastructure they and others rely on to learn technology across time, this dissertation challenges deficit models of aging premised on decline and disengagement. Public libraries and senior centers are overpressured, publicly funded institutions. By embracing the agency of older adults, these institutions could reconfigure themselves for an information society that is aging

Precedence-constrained scheduling problems parameterized by partial order width

Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1-2):533-562), we show that P2|prec,$p_j{\in}\{1,2\}$|$C_{\max}$, the problem of finding a non-preemptive minimum-makespan schedule for precedence-constrained jobs of lengths 1 and 2 on two parallel identical machines, is W[2]-hard parameterized by the width of the partial order giving the precedence constraints. To this end, we show that Shuffle Product, the problem of deciding whether a given word can be obtained by interleaving the letters of $k$ other given words, is W[2]-hard parameterized by $k$, thus additionally answering a question posed by Rizzi and Vialette (CSR 2013). Finally, refining a geometric algorithm due to Servakh (Diskretn. Anal. Issled. Oper. 7(1):75-82), we show that the more general Resource-Constrained Project Scheduling problem is fixed-parameter tractable parameterized by the partial order width combined with the maximum allowed difference between the earliest possible and factual starting time of a job.Comment: 14 pages plus appendi

Dynamics of modal power distribution in a multimode semiconductor laser with optical feedback

The dynamics of power distribution between longitudinal modes of a multimode semiconductor laser subjected to external optical feedback is experimentally analyzed in the low-frequency fluctuation regime. Power dropouts in the total light intensity are invariably accompanied by sudden activations of several longitudinal modes. These activations are seen not to be simultaneous to the dropouts, but to occur after them. The phenomenon is statistically analysed in a systematic way, and the corresponding delay is estimated.Comment: 3 pages, 4 figures, revte