scholarly journals Phenomenological implications of Bohr space in six dimensions

2019 ◽  
Vol 21 ◽  
pp. 75
Author(s):  
P. Georgoudis
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Mass Parameter ◽  
Structural Evolution ◽  
Second Order ◽  
Irrotational Flow ◽  
Atomic Nuclei ◽  
Six Dimensions ◽  
Shape Phase Transition

The critical point for a second order shape/phase transition in the structural evolution of atomic nuclei, the consequences on the mass parameter and its irrotational flow are discussed after the embedding of Bohr space in six dimensions.

scholarly journals Variational procedure leading from Davidson potentials to the E(5)and X(5) critical point symmetries

2020 ◽  
Vol 13 ◽  
pp. 10
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
N. Minkov ◽  
D. Petrellis ◽  
P. P. Raychev ◽  
...  
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Ground State ◽  
Nuclear Energy ◽  
Energy Spectra ◽  
Variational Procedure ◽  
Ground State Band ◽  
Sharp Maximum ◽  
State Band ◽  
Shape Phase Transition

Davidson potentials of the form β^2 + β0^4/β^2, when used in the original Bohr Hamiltonian for γ-independent potentials bridge the U(5) and 0(6) symmetries. Using a variational procedure, we determine for each value of angular momentum L the value of β0 at which the derivative of the energy ratio RL = E(L)/E(2) with respect to β0 has a sharp maximum, the collection of RL values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to Ο(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

Extended study on the application of the sextic potential in the frame of X(3)-Sextic

2021 ◽  
Author(s):  
Mostafa Oulne ◽  
Imad Tagdamte
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Electromagnetic Properties ◽  
Shape Evolution ◽  
Isotopic Chain ◽  
Oscillator Potential ◽  
Extended Study ◽  
Deformed Nuclei ◽  
Exact Solvability ◽  
Shape Phase Transition

Abstract The main aim of the present paper is to study extensively the γ-rigid Bohr Hamiltonian with anharmonic sextic oscillator potential for the variable β and γ = 0. For the corresponding spectral problem, a finite number of eigenvalues are found explicitly, by algebraic means, so-called Quasi-Exact Solvability (QES). The evolution of the spectral and electromagnetic properties by considering higher exact solvability orders is investigated, especially the approximate degeneracy of the ground and first two β bands in the critical point of the shape phase transition from a harmonic to an anharmonic prolate β-soft, also the shape evolution within an isotopic chain. Numerical results are given for 39 nuclei, namely, 98-108Ru, 100-102Mo, 116-130Xe, 180-196Pt, 172Os, 146-150Nd, 132-134Ce, 152-154Gd, 154-156Dy, 150-152Sm, 190Hg and 222Ra. Across this study, it seems that the higher quasi-exact solvability order improves our results by decreasing the rms, mostly for deformed nuclei. The nuclei 100,104Ru, 118,120,126,128Xe, 148Nd and 172Os fall exactly in the critical point.

scholarly journals Low- Z boundary of the N=88 –90 shape phase transition: Ce148 near the critical point

2020 ◽  
Vol 101 (1) ◽  
Author(s):  
P. Koseoglou ◽  
V. Werner ◽  
N. Pietralla ◽  
S. Ilieva ◽  
T. Nikšić ◽  
...  
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Shape Phase Transition

scholarly journals Big Bang as a Critical Point

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Jakub Mielczarek
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Quantum Gravity ◽  
Critical Point ◽  
Order Phase Transition ◽  
Big Bang ◽  
Second Order ◽  
Extended Phase ◽  
Causal Dynamical Triangulations ◽  
Second Order Phase Transition

This article addresses the issue of possible gravitational phase transitions in the early universe. We suggest that a second-order phase transition observed in the Causal Dynamical Triangulations approach to quantum gravity may have a cosmological relevance. The phase transition interpolates between a nongeometric crumpled phase of gravity and an extended phase with classical properties. Transition of this kind has been postulated earlier in the context of geometrogenesis in the Quantum Graphity approach to quantum gravity. We show that critical behavior may also be associated with a signature change in Loop Quantum Cosmology, which occurs as a result of quantum deformation of the hypersurface deformation algebra. In the considered cases, classical space-time originates at the critical point associated with a second-order phase transition. Relation between the gravitational phase transitions and the corresponding change of symmetry is underlined.

scholarly journals Generalized Ehrenfest's equations and phase transition in black holes

2015 ◽  
Vol 24 (03) ◽  
pp. 1550029 ◽  
Author(s):  
Mohammad Bagher Jahani Poshteh ◽  
Behrouz Mirza ◽  
Fatemeh Oboudiat
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Critical Point ◽  
Order Phase Transition ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Second Order ◽  
First Law Of Thermodynamics ◽  
Three Degrees Of Freedom ◽  
Second Order Phase Transition

In this paper, we generalize Ehrenfest's equations to systems having two work terms, i.e. systems with three degrees of freedom. For black holes with two work terms we obtain nine equations instead of two to be satisfied at the critical point of a second-order phase transition. We finally generalize this method to a system with an arbitrary number of degrees of freedom and found there is [Formula: see text] equations to be satisfied at the point of a second-order phase transition where N is number of work terms in the first law of thermodynamics.

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