Liouville-von Neumann approach and time-dependent Gaussian approximation

We show that Liouville-von Neumann approach to quantum mechanical systems, which demands the existence of invariant operators, reproduces the time-dependent variational Gaussian approximation. We find the effective action of the time-dependent systems and show that many aspects of the dynamics are independent of the details of time evolution, e.g., the squeezing of the wave-function is determined by the effective potential of the final stage of time-evolution.Comment: 10 pages, 2 figure

A case study in sustainability: designing studio spaces on the vertical within the recycled Armory Building

In a period of scarce resources, this proposal presents a plan for adapting an existing facility for an optimum resource investment. The moral obligation of the interior designer is, not only to develop a design in a new space, but also to preserve previously built environments. The most important contemporary issue is to create an environmentally friendly design. Therefore, the designer needs to consider environmental aspects, which are energy conservation, pollution prevention, resource efficiency, systems integration, and life cycle cost. This proposal will encompass a sustainable design, as well as functional, efficient and aesthetic environments. The College of Design on the Iowa State University campus operates two buildings as design facilities: The Design Center and the Armory Building. The Armory Building, with studios and presentation space for freshmen of the Core Program (Pre-professional programs), is being used as a facility to support the Design Center. The proposed four level design for the Armory will occupy the central space of the building. It will house design studios for the graduate programs and Core program, faculty-student research spaces, computer and lighting labs, lecture and presentation spaces, plus an auditorium, activity space, and lounges. This proposed design would consider health and safety, welfare, fire and ADA codes; due to all of these needs, an elevator and three two-hour rated staircases will be included in the design. It is of utmost importance to utilize ecological materials in the proposed project. Therefore, the purpose necessitates the use of sustainable materials, appropriate spaces where they are used, and the reasons they are so specified. It is believed that this design will make use of sustainable materials for reducing environmental impact based on a green building rating system. The main purpose of the present study is to design and develop an educational facility in the Armory Building, utilizing sustainable design materials. The proposed design will include preservation of the historical building, improvement of educational environment, and the utilization of the sustainable principles. This present proposal study is directed to achieving a design approach through the creation of a new conceptual design for the Armory Building

Casimir energy of a spherical shell in κ−\kappa-Minkowski spacetime

We study the Casimir energy of a spherical shell of radius $a$ in $\kappa$-Minkowski spacetime for a complex field with an asymmetric ordering and obtain the energy up to $O(1/\kappa^2)$. We show that the vacuum breaks particle and anti-particle symmetry if one requires the spectra to be consistent with the blackbody radiation at the commutative limit.Comment: 23 pages, 3 figures, add more analysi

Smeared BTZ Black Hole from Space Noncommutativity

We study a novel phenomena of smearing of black hole horizons from the effect of space noncommutativity. We present an explicit example in $AdS_3$ space, using the Chern-Simons formulation of gravity. This produces a smeared BTZ black hole which goes beyond the classical spacetime unexpectedly and there is {\it no} reality problem in our approach with the gauge group $U(1,1) \times U(1,1)$. The horizons are smeared, due to a splitting of the Killing horizon and the apparent horizon, and there is a metric signature change to Euclidean in the smeared region. The inner boundary of the smeared region acts as a trapped surface for timelike particles but the outer as a classical barrier for ingoing particles. The lightlike signals can escape from or reach the smeared region in a {\it finite} time, which indicates that {\it the black hole is not so dark, even classically.} In addition, it is remarked that the Hawking temperature can {\it not} be defined by the regularity in the Euclidean geometry except in the non-rotating case, and the origin can be smeared by a {\it new} (apparent) horizon.Comment: Added notes about boundary conditions, NC curvature, and torsion; Accepted in JHE

Constant-Factor Approximation Algorithms for the Parity-Constrained Facility Location Problem

Facility location is a prominent optimization problem that has inspired a large quantity of both theoretical and practical studies in combinatorial optimization. Although the problem has been investigated under various settings reflecting typical structures within the optimization problems of practical interest, little is known on how the problem behaves in conjunction with parity constraints. This shortfall of understanding was rather discouraging when we consider the central role of parity in the field of combinatorics. In this paper, we present the first constant-factor approximation algorithm for the facility location problem with parity constraints. We are given as the input a metric on a set of facilities and clients, the opening cost of each facility, and the parity requirement - odd, even, or unconstrained - of every facility in this problem. The objective is to open a subset of facilities and assign every client to an open facility so as to minimize the sum of the total opening costs and the assignment distances, but subject to the condition that the number of clients assigned to each open facility must have the same parity as its requirement. Although the unconstrained facility location problem as a relaxation for this parity-constrained generalization has unbounded gap, we demonstrate that it yields a structured solution whose parity violation can be corrected at small cost. This correction is prescribed by a T-join on an auxiliary graph constructed by the algorithm. This auxiliary graph does not satisfy the triangle inequality, but we show that a carefully chosen set of shortcutting operations leads to a cheap and sparse T-join. Finally, we bound the correction cost by exhibiting a combinatorial multi-step construction of an upper bound