Theory of Brueckner and Sawada Applied to a Many-Boson Model

1973 ◽  
Vol 51 (3) ◽  
pp. 292-301 ◽  
Author(s):  
M. Razavy ◽  
E. S. Krebes
Keyword(s):  
Ground State ◽  
Transition Point ◽  
Matrix Formalism ◽  
Coupling Constant ◽  
Bogoliubov Approximation ◽  
Wide Range ◽  
Simple Change ◽  
Boson Model ◽  
Repulsive Forces ◽  
Range Of Values

The Bassichis–Foldy model of a simple interacting boson is solved numerically and the results are compared with those obtained by the Bogoliubov approximation and by the Brueckner–Sawada t-matrix formalism. In the normal region, contrary to the widely held view, the Brueckner–Sawada approximation for the energy of the ground state is not reliable for strong, well-behaved, repulsive forces. The Bogoliubov approximation, on the other hand, remains valid for a wide range of values of the coupling constant. In the inverted region, the attractive force causes a population inversion in the levels of the system. For this case a modified Brueckner–Sawada approximation is developed. This method is applied to the calculation of the transition point and the energies of the ground and the first excited states of the system. Here most of the predictions of the modified Brueckner–Sawada approximation are quite accurate. By a simple change in the Bassichis–Foldy model it is shown that even, for two bosons there can be a phase transition. In this model, the derivative of the ground state energy with respect to the coupling constant is discontinuous at the transition point.

scholarly journals On Existence of Ground States in the Spin Boson Model

2021 ◽  
Author(s):  
David Hasler ◽  
Benjamin Hinrichs ◽  
Oliver Siebert
Keyword(s):  
Magnetic Field ◽  
Ground State ◽  
State Energy ◽  
Ground States ◽  
Second Derivative ◽  
Coupling Constant ◽  
Infrared Regularization ◽  
Massless Spin ◽  
Boson Model ◽  
Constant External Magnetic Field

AbstractWe show the existence of ground states in the massless spin boson model without any infrared regularization. Our proof is non-perturbative and relies on a compactness argument. It works for arbitrary values of the coupling constant under the hypothesis that the second derivative of the ground state energy as a function of a constant external magnetic field is bounded.

scholarly journals Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 77
Author(s):  
Angus J. Dunnett ◽  
Alex W. Chin
Keyword(s):  
Finite Temperature ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Matrix Product ◽  
Open Quantum ◽  
Matrix Product State ◽  
Wide Range ◽  
Boson Model ◽  
Non Equilibrium

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

scholarly journals Entanglement entropy in cubic gravitational theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Elena Cáceres ◽  
Rodrigo Castillo Vásquez ◽  
Alejandro Vilar López
Keyword(s):  
Entanglement Entropy ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Holographic Entanglement Entropy ◽  
Gravitational Theories ◽  
Entropy Functional ◽  
Wide Range ◽  
Splitting Problem ◽  
Range Of Values

Abstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

scholarly journals A Comparison of Some Methods of Deriving the Instantaneous Unit Hydrograph

1985 ◽  
Vol 16 (1) ◽  
pp. 1-10 ◽  
Author(s):  
V. P. Singh ◽  
C. Corradini ◽  
F. Melone
Keyword(s):  
Peak Flow ◽  
Central Italy ◽  
Effective Rainfall ◽  
Unit Hydrograph ◽  
Time To Peak ◽  
Wide Range ◽  
Instantaneous Unit Hydrograph ◽  
Similar Accuracy ◽  
Two Parameters ◽  
Range Of Values

The geomorphological instantaneous unit hydrograph (IUH) proposed by Gupta et al. (1980) was compared with the IUH derived by commonly used time-area and Nash methods. This comparison was performed by analyzing the effective rainfall-direct runoff relationship for four large basins in Central Italy ranging in area from 934 to 4,147 km2. The Nash method was found to be the most accurate of the three methods. The geomorphological method, with only one parameter estimated in advance from the observed data, was found to be little less accurate than the Nash method which has two parameters determined from observations. Furthermore, if the geomorphological and Nash methods employed the same information represented by basin lag, then they produced similar accuracy provided the other Nash parameter, expressed by the product of peak flow and time to peak, was empirically assessed within a wide range of values. It was concluded that it was more appropriate to use the geomorphological method for ungaged basins and the Nash method for gaged basins.

Lubricating motion of a sphere towards a thin porous slab with Saffman slip condition

2019 ◽  
Vol 867 ◽  
pp. 949-968 ◽  
Author(s):  
Sondes Khabthani ◽  
Antoine Sellier ◽  
François Feuillebois
Keyword(s):  
Slip Length ◽  
Solid Sphere ◽  
Slip Condition ◽  
Darcy Law ◽  
Slab Thickness ◽  
Wide Range ◽  
Sphere Radius ◽  
Permeability Parameter ◽  
Interface Slip ◽  
Range Of Values

Near-contact hydrodynamic interactions between a solid sphere and a plane porous slab are investigated in the framework of lubrication theory. The size of pores in the slab is small compared with the slab thickness so that the Darcy law holds there. The slab is thin: that is, its thickness is small compared with the sphere radius. The considered problem involves a sphere translating above the slab together with a permeation flow across the slab and a uniform pressure below. The pressure is continuous across both slab interfaces and the Saffman slip condition applies on its upper interface. An extended Reynolds-like equation is derived for the pressure in the gap between the sphere and the slab. This equation is solved numerically and the drag force on the sphere is calculated therefrom for a wide range of values of the slab interface slip length and of the permeability parameter $\unicode[STIX]{x1D6FD}=24k^{\ast }R/(e\unicode[STIX]{x1D6FF}^{2})$, where $k^{\ast }$ is the permeability, $e$ is the porous slab thickness, $R$ is the sphere radius and $\unicode[STIX]{x1D6FF}$ is the gap. Moreover, asymptotics expansions for the pressure and drag are derived for high and low $\unicode[STIX]{x1D6FD}$. These expansions, which agree with the numerics, are also handy formulae for practical use. All results match with those of other authors in particular cases. The settling trajectory of a sphere towards a porous slab in a fluid at rest is calculated from these results and, as expected, the time for reaching the slab decays for increasing slab permeability and upper interface slip length.

The State of the Art of Rubber-Seal Technology

1987 ◽  
Vol 60 (3) ◽  
pp. 381-416 ◽  
Author(s):  
B. S. Nau
Keyword(s):  
State Of The Art ◽  
Test Procedure ◽  
Working Party ◽  
The State ◽  
Supporting Evidence ◽  
Wide Range ◽  
Lip Seals ◽  
Alternative Hypotheses ◽  
Series Of Experiments ◽  
Range Of Values

Abstract The understanding of the engineering fundamentals of rubber seals of all the various types has been developing gradually over the past two or three decades, but there is still much to understand, Tables V–VII summarize the state of the art. In the case of rubber-based gaskets, the field of high-temperature applications has scarcely been touched, although there are plans to initiate work in this area both in the U.S.A. at PVRC, and in the U.K., at BHRA. In the case of reciprocating rubber seals, a broad basis of theory and experiment has been developed, yet it still is not possible to design such a seal from first principles. Indeed, in a comparative series of experiments run recently on seals from a single batch, tested in different laboratories round the world to the same test procedure, under the aegis of an ISO working party, a very wide range of values was reported for leakage and friction. The explanation for this has still to be ascertained. In the case of rotary lip seals, theories and supporting evidence have been brought forward to support alternative hypotheses for lubrication and sealing mechanisms. None can be said to have become generally accepted, and it remains to crystallize a unified theory.

SUPER SYMMETRY IN STRONG AND WEAK INTERACTIONS

2010 ◽  
Vol 19 (02) ◽  
pp. 263-280
Author(s):  
U. V. S. SESHAVATHARAM ◽  
S. LAKSHMINARAYANA
Keyword(s):  
Ground State ◽  
Crucial Role ◽  
Weak Interactions ◽  
Light Quark ◽  
Fermion Mass ◽  
Coupling Constant ◽  
Mass Generation ◽  
Super Symmetry ◽  
Charged Boson ◽  
Charged Mesons

For strong interaction two new fermion mass units 105.32 MeV and 11450 MeV are assumed. Existence of "Integral charge quark bosons", "Integral charge effective quark fermions", "Integral charge (effective) quark fermi-gluons" and "Integral charge quark boso-gluons" are assumed and their masses are estimated. It is noticed that, characteristic nuclear charged fermion is Xs · 105.32 = 938.8 MeV and corresponding charged boson is Xs(105.32/x) = 415.0 where Xs = 8.914 is the inverse of the strong coupling constant and x = 2.26234 is a new number by using which "super symmetry" can be seen in "strong and weak" interactions. 11450 MeV fermion and its boson of mass = 11450/x = 5060 MeV plays a crucial role in "sub quark physics" and "weak interaction". 938.8 MeV strong fermion seems to be the proton. 415 MeV strong boson seems to be the mother of the presently believed 493,496 and 547 MeV etc, strange mesons. With 11450 MeV fermion "effective quark-fermi-gluons" and with 5060 MeV boson "quark boso-gluon masses" are estimated. "Effective quark fermi-gluons" plays a crucial role in ground state charged baryons mass generation. Light quark bosons couple with these charged baryons to form doublets and triplets. "Quark boso-gluons" plays a crucial role in ground state neutral and charged mesons mass generation. Fine and super-fine rotational levels can be given by [I or (I/2)] power(1/4) and [I or (I/2)] power(1/12) respectively. Here, I = n(n+1) and n = 1, 2, 3, ….

scholarly journals Framing the Values of Vernacular Architecture for a Value-Based Conservation: A Conceptual Framework

2021 ◽  
Vol 13 (9) ◽  
pp. 4974
Author(s):  
Obafemi A. P. Olukoya
Keyword(s):  
Vernacular Architecture ◽  
Conservation Strategy ◽  
Participatory Process ◽  
Value Assessment ◽  
A Value ◽  
Wide Range ◽  
Flexible Framework ◽  
Value Model ◽  
Contextual Values ◽  
Range Of Values

While a growing number of researchers have provided series of tough critiques of the typology-led heritage value assessment over the recent years, the impacts have been constrained by the continued obsession with expanding the list of the predetermined value typologies rather than escaping its limitations. While these sustained debates have provided important insights, this article argues that operationalizing these predetermined ‘one-size-fits-all’ value typologies is symptomatic of a number of shortcomings, especially in the context of capturing the pluralities of values in contextualized heritage such as vernacular architecture. It also often undermines inclusivity and participation in the valuing processes. However, rather than simply rejecting the values-based paradigm, this article proposes a conceptual value assessment framework that is informed by the theorization of vernacular architecture as a contextualized heritage. The proposed Vernacular Value Model (VVM) puts forward the ‘when(s)’ and ‘how(s)’ of amalgamating both technical and normative processes to capture the range of contextual values present in built vernacular heritage. To this end, this article posits that by drawing on such a proposed flexible framework, the conservation strategy for built vernacular heritage can be propagated as an inclusive and participatory process which captures the wide range of values for a more sustainable practices for conservation.

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