scholarly journals Free energy and entropy for an impurity in a periodic background in one dimension

2020 ◽  
Vol 28 (2) ◽  
pp. 29-38
Author(s):  
M. Bordag ◽  
I. G. Pirozhenko
Keyword(s):  
Free Energy ◽  
One Dimension ◽  
Single Impurity ◽  
Delta Functions

In this paper, we continue our study of periodic lattices formed by delta functions and their derivatives in (1+1) dimensions. Such systems are interesting as allowing for investigation of complicated problems in quite simple terms. Specifically, we consider the free energy of a single impurity in the background of such lattice. After developing the necessary technical tools, we consider as an example a specific case and found that the free energy shows a non monotone behavior as function of the temperature.

scholarly journals BABY UNIVERSES AND STRING THEORY

2006 ◽  
Vol 15 (10) ◽  
pp. 1581-1586 ◽  
Author(s):  
ROBBERT DIJKGRAAF ◽  
RAJESH GOPAKUMAR ◽  
HIROSI OOGURI ◽  
CUMRUN VAFA
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
String Theory ◽  
Quantum Gravity ◽  
One Dimension ◽  
Free Fermions ◽  
Yang Mills ◽  
Exact Answer ◽  
Exactly Solvable ◽  
Baby Universes

The description of 4D BPS black holes in terms of branes wrapped on various cycles in a Calabi–Yau space gives us the opportunity to study various issues in quantum gravity in a definite way by means of the worldvolume theory of the branes. In the particular example discussed here, there is a simple worldvolume description in terms of 2D Yang–Mills theory. The latter is an exactly solvable system of free fermions in one dimension. The exact answer for the free energy of this system can be written in a way that suggests an interpretation in terms of contributions from multiple (baby) universes.

scholarly journals Free energy asymptotics of the quantum Heisenberg spin chain

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Marcin Napiórkowski ◽  
Robert Seiringer
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Upper And Lower Bounds ◽  
One Dimension ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Analogous Estimate ◽  
Spatial Dimensions ◽  
The One ◽  
Ideal Bose Gas

AbstractWe consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin $$S\ge 1/2$$ S ≥ 1 / 2 . We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.

scholarly journals SCALING VIOLATION IN O(N) VECTOR MODELS

1994 ◽  
Vol 09 (07) ◽  
pp. 631-641 ◽  
Author(s):  
SHINSUKE NISHIGAKI
Keyword(s):  
Free Energy ◽  
Random Walk ◽  
Vector Field ◽  
Cayley Tree ◽  
Scaling Limit ◽  
Field Theories ◽  
One Dimension ◽  
Polymeric Systems ◽  
N Vector ◽  
Double Scaling Limit

We investigate O(N)-symmetric vector field theories in the double scaling limit. Our model describes branched polymeric systems in D dimensions, whose multicritical series interpolates between the Cayley tree and the ordinary random walk. We give explicit forms of residual divergences in the free energy, analogous to those observed in the strings in one dimension.

scholarly journals The Finite Temperature Effective Potential for Local Composite Operators

1997 ◽  
Vol 12 (14) ◽  
pp. 1003-1010 ◽  
Author(s):  
Anna Okopińska
Keyword(s):  
Free Energy ◽  
Effective Potential ◽  
Finite Temperature ◽  
Anharmonic Oscillator ◽  
Exact Result ◽  
One Dimension ◽  
Successive Approximations ◽  
Quantum Field ◽  
Effective Coupling ◽  
Scalar Quantum

The method of the effective action for the composite operators Φ2(x) and Φ4(x) is applied to the thermodynamics of the scalar quantum field with λΦ4 interaction. An expansion of the finite temperature effective potential in powers of ℏ provides successive approximations to the free energy with an effective mass and an effective coupling determined by the gap equations. The numerical results are studied in the spacetime of one dimension when the theory is equivalent to the quantum mechanics of an anharmonic oscillator. The approximations to the free energy show quick convergence to the exact result.

Center deviation of localized modes in a one-dimension anharmonic single impurity chain

2018 ◽  
Vol 534 ◽  
pp. 22-25
Author(s):  
Xuan-Lin Chen ◽  
Gang-Bei Zhu ◽  
Ze-Hui Jiang ◽  
Yan-Qiang Yang
Keyword(s):  
One Dimension ◽  
Localized Modes ◽  
Single Impurity

Encultured minds, not error reduction minds

2020 ◽  
Vol 43 ◽  
Author(s):  
Robert Mirski ◽  
Mark H. Bickhard ◽  
David Eck ◽  
Arkadiusz Gut
Keyword(s):  
Free Energy ◽  
Error Reduction ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Current Article

Abstract There are serious theoretical problems with the free-energy principle model, which are shown in the current article. We discuss the proposed model's inability to account for culturally emergent normativities, and point out the foundational issues that we claim this inability stems from.

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

Quantitative Diameter Measurements of Chromatin and TMV Fibers in the Freeze-Dried State

1988 ◽  
Vol 46 ◽  
pp. 170-171
Author(s):  
B. D. Athey ◽  
A. L. Stout ◽  
M. F. Smith ◽  
J. P. Langmore
Keyword(s):  
Reliable Method ◽  
Fiber Diameter ◽  
Quantitative Agreement ◽  
One Dimension ◽  
Fiber Axis ◽  
Two Dimensional ◽  
Fiber Density ◽  
Variable Diameter ◽  
Freeze Dried ◽  
Expected Values

Although there is general agreement that Inactive chromosome fibers consist of helically packed nucleosomes, the pattern of packing is still undetermined. Only one of the proposed models, the crossed-linker model, predicts a variable diameter dependent on the length of DNA between nucleosomes. Measurements of the fiber diameter of negatively-stained and frozen- hydrated- chromatin from Thyone sperm (87bp linker) and Necturus erythrocytes (48bp linker) have been previously reported from this laboratory. We now introduce a more reliable method of measuring the diameters of electron images of fibrous objects. The procedure uses a modified version of the computer program TOTAL, which takes a two-dimensional projection of the fiber density (represented by the micrograph itself) and projects it down the fiber axis onto one dimension. We illustrate this method using high contrast, in-focus STEM images of TMV and chromatin from Thyone and Necturus. The measured diameters are in quantitative agreement with the expected values for the crossed-linker model for chromatin structure

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