BOUND STATES IN GRAPHENE

2009 ◽  
Vol 24 (02) ◽  
pp. 99-107 ◽  
Author(s):  
KUMAR S. GUPTA ◽  
SIDDHARTHA SEN
Keyword(s):  
Bound States ◽  
Interaction Strength ◽  
Critical Value ◽  
Oscillatory Behaviour ◽  
System Parameters ◽  
Quantum Analysis ◽  
Subcritical Region ◽  
Charge Impurity ◽  
A Charge ◽  
Group Flow

We present a quantum analysis of the massless excitations in graphene with a charge impurity. When the effective charge exceeds a certain critical value, the spectrum is quantised and unbounded from below. The corresponding eigenstates are square-integrable at infinity and have a rapidly oscillatory behaviour in the short distance, which can be interpreted as a fall to the centre. Using a cutoff regularisation, we show that the effective Coulomb interaction strength is driven to its critical value under the renormalisation group flow. In the subcritical region, we find bound states with imaginary values of the energy for certain range of the system parameters. The physical significance of these bound states with imaginary eigenvalues is discussed.

Tight-binding method for pseudoatoms based on the Bloch density matrix

1968 ◽  
Vol 304 (1476) ◽  
pp. 99-112 ◽  
Keyword(s):  
Partition Function ◽  
Density Matrix ◽  
Bound States ◽  
Order Approximation ◽  
Tight Binding ◽  
Fermi Gas ◽  
Zero Order Approximation ◽  
Potential Matrix ◽  
A Charge ◽  
Scattering Centre

Recent work by Hilton, March & Curtis (1967) has shown how the Bloch density matrix may be calculated for an attractive scattering centre in a Fermi gas which is strong enough to lead to bound states. Using this pseudoatom description, and expressing the zero order approximation of independent pseudoatoms by writing the total partition function as a product of the single-centre functions, we develop a systematic procedure for calculating energy band structures. The convergence of the method depends on the magnitude of the overlaps of the effective potential matrix U introduced by Hilton, March & Curtis, for pseudoatoms on adjacent sites. To illustrate the method, calculation of the partition function of metallic Be is carried out from the earlier one-centre results for a charge Z = 4 in a Fermi gas. A preliminary estimate of the density of states in Be is reported, from this partition function.

scholarly journals Quantum stabilization of cosmic strings

2015 ◽  
Vol 30 (27) ◽  
pp. 1530022 ◽  
Author(s):  
H. Weigel ◽  
M. Quandt ◽  
N. Graham
Keyword(s):  
Standard Model ◽  
Top Quark ◽  
Cosmic String ◽  
Bound States ◽  
Degrees Of Freedom ◽  
Energy Levels ◽  
Binding Energies ◽  
Fermion Mass ◽  
The Standard Model ◽  
A Charge

In the standard model, stabilization of a classically unstable cosmic string may occur through the quantum fluctuations of a heavy fermion doublet. We review numerical results from a semiclassical expansion in a reduced version of the standard model. In this expansion, the leading quantum corrections emerge at one loop level for many internal degrees of freedom. The resulting vacuum polarization energy and the binding energies of occupied fermion energy levels are of the same order, and must therefore be treated on equal footing. Populating these bound states lowers the total energy compared to the same number of free fermions and assigns a charge to the string. Charged strings are already stabilized for a fermion mass only somewhat larger than the top quark mass. Though obtained in a reduced version, these results suggest that neither extraordinarily large fermion masses nor unrealistic couplings are required to bind a cosmic string in the standard model. Furthermore, we also review results for a quantum stabilization mechanism that prevents closed Nielsen–Olesen-type strings from collapsing.

scholarly journals Dual Negative Differential of Heat Generation in a Strongly Correlated Quantum Dot Side-Coupled to Majorana Bound States

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhu-Hua Wang ◽  
Wen-Cheng Huang
Keyword(s):  
Quantum Dot ◽  
Heat Generation ◽  
Coulomb Blockade ◽  
Bound States ◽  
Interaction Strength ◽  
Local Heat ◽  
Transport Processes ◽  
Strongly Correlated ◽  
Majorana Bound States ◽  
Coulomb Blockade Regime

We study theoretically the properties of local heat originated from energy exchange between electrons passing through a quantum dot (QD) coupled to a phonon bath. The dot is sandwiched between two normal metal leads and also side-coupled to Majorana bound states (MBSs) formed at opposite ends of a topological superconductor nanowire. We find that in addition to the negative differential of heat generation (NDHG) in the Coulomb blockade regime, another NDHG emerges near the leads’ Fermi level due to the dot-MBS coupling. This dual NDHG effect is robust against the variation of intradot Coulomb interaction strength, and disappears if the QD is coupled to regular Fermions. Direct hybridization between the MBSs reduces their impacts on the electronic transport processes, and eliminates the dual NDHG effect. Our results show that the dual NDHG effect is quite efficient for inferring the existence of MBSs, and may remedy some limitations of the detection schemes relying on tunneling spectroscopy technique.

Quantum signature of breathers in 1D ultracold bosons in optical lattices involving next-nearest neighbor interactions

2017 ◽  
Vol 31 (20) ◽  
pp. 1750140 ◽  
Author(s):  
Z. I. Djoufack ◽  
A. Kenfack-Jiotsa ◽  
J.-P. Nguenang
Keyword(s):  
Energy Spectrum ◽  
Optical Lattice ◽  
Bound States ◽  
Optical Lattices ◽  
Nearest Neighbor ◽  
Laser Light ◽  
Energy Spectra ◽  
System Parameters ◽  
Quantum Breathers ◽  
Bosonic Atoms

The dynamics and the energy spectrum of an ultracold gas of bosonic atoms in an optical lattice can be described by a Bose–Hubbard model for which the system parameters can be controlled by laser light. We study by means of the perturbation theory in addition to the numerical diagonalization, the energy spectrum and the related features of the band structures of the ultracold bosons in optical lattices containing a few number of quanta interacting with next-nearest neighbor interactions (NNNI) modeled by the Bose–Hubbard Hamiltonian. The energy spectra of such system display the bound states signature, which are analyzed in the first Brillouin zone for different wave numbers. The finding, i.e., quantum breathers, shows that their probabilities’ weight depends on the wave vector. The influence of NNNI on both the probabilities’ amplitude and the correlation function is also realized in case of a system with a small number of sites, respectively.

scholarly journals On the Discrete Spectrum of a Model Operator in Fermionic Fock Space

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Zahriddin Muminov ◽  
Fudziah Ismail ◽  
Zainidin Eshkuvatov ◽  
Jamshid Rasulov
Keyword(s):  
Bound States ◽  
Fock Space ◽  
Critical Value ◽  
Efimov Effect ◽  
Model Operator ◽  
The Third ◽  
Direct Sum ◽  
Friedrichs Model ◽  
Number Of Particles ◽  
Generalized Friedrichs Model

We consider a model operatorHassociated with a system describing three particles in interaction, without conservation of the number of particles. The operatorHacts in the direct sum of zero-, one-, and two-particle subspaces of thefermionic Fock space ℱa(L2(𝕋3))overL2(𝕋3). We admit a general form for the "kinetic" part of the HamiltonianH, which contains a parameterγto distinguish the two identical particles from the third one. (i) We find a critical valueγ*for the parameterγthat allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance) and we prove that only forγ<γ*the Efimov effect is absent, while this effect exists for anyγ>γ*. (ii) In the caseγ>γ*, we also establish the following asymptotics for the numberN(z)of eigenvalues ofHbelowz<Emin=infσessH:limz→EminNz/logEmin-z=𝒰0γ  𝒰0γ>0, for allγ>γ*.

LANDAU POLES, ULTRAVIOLET FIXED POINTS, AND “TRIVIALITY” IN THE PERTURBATIVE EXPANSION OF (λΦ4)4

1996 ◽  
Vol 11 (31) ◽  
pp. 2511-2524 ◽  
Author(s):  
M. CONSOLI ◽  
P.M. STEVENSON
Keyword(s):  
Fixed Points ◽  
Higgs Mass ◽  
Interaction Strength ◽  
Continuum Theory ◽  
Perturbative Approach ◽  
The Standard Model ◽  
Physical Mass ◽  
Group Flow ◽  
Scalar Sector ◽  
The Continuum

The “triviality” of (λΦ4)4 means that the continuum theory has a vanishing renormalized coupling λR. This result inherently conflicts with the standard perturbative approach, which begins by postulating a nonzero, cutoff-independent λR, and which suffers from pathologies — either Landau poles (in odd orders) or spurious ultraviolet fixed points (in even orders). We show how the known structure of perturbation theory can be rearranged, to arbitrarily high orders, to fulfil the condition λR=0. The corresponding renormalization group flow of the bare coupling coincides with that needed to renormalize the effective potential, as calculated in any “triviality”-compatible approximation. Although λR vanishes, the physical mass is finite; there is no proportionality between the two. That implies that the Higgs mass does not represent a measure of the observable interaction strength in the scalar sector of the standard model.

scholarly journals Big Bang nucleosynthesis with long-lived strongly interacting relic particles

2009 ◽  
Vol 5 (S268) ◽  
pp. 33-38
Author(s):  
Motohiko Kusakabe ◽  
Toshitaka Kajino ◽  
Takashi Yoshida ◽  
Grant J. Mathews
Keyword(s):  
Beta Decay ◽  
Bound States ◽  
Nuclear Reactions ◽  
Interaction Strength ◽  
Light Element ◽  
Big Bang ◽  
Heavy Elements ◽  
Big Bang Nucleosynthesis ◽  
Element Abundances ◽  
Strongly Interacting

AbstractWe study effects of relic long-lived strongly interacting massive particles (X particles) on big bang nucleosynthesis (BBN). The X particle is assumed to have existed during the BBN epoch, but decayed long before detected. The interaction strength between an X and a nucleon is assumed to be similar to that between nucleons. Rates of nuclear reactions and beta decay of X-nuclei are calculated, and the BBN in the presence of neutral charged X0 particles is calculated taking account of captures of X0 by nuclei. As a result, the X0 particles form bound states with normal nuclei during a relatively early epoch of BBN leading to the production of heavy elements. Constraints on the abundance of X0 are derived from observations of primordial light element abundances. Particle models which predict long-lived colored particles with lifetimes longer than ~200 s are rejected. This scenario prefers the production of 9Be and 10B. There might, therefore, remain a signature of the X particle on primordial abundances of those elements. Possible signatures left on light element abundances expected in four different models are summarized.

scholarly journals IMPACT DYNAMICS OF LARGE DIMENSIONAL SYSTEMS

2007 ◽  
Vol 17 (02) ◽  
pp. 561-573 ◽  
Author(s):  
M. E. HOMER ◽  
S. J. HOGAN
Keyword(s):  
Numerical Simulation ◽  
Probability Theory ◽  
Simple Model ◽  
Critical Value ◽  
Impact Dynamics ◽  
Global Dynamics ◽  
System Parameters ◽  
Repeated Impacts ◽  
Sudden Jump ◽  
Good Agreement

In this paper we present a model of impact dynamics in large dimensional systems. We describe a hybrid method, based on graph theory and probability theory, which enables us qualitatively to model the statistics of global dynamics as parameters are varied. Direct numerical simulation reveals a sudden jump from no impacts within the system to many repeated impacts at a critical value of system parameters. We show that a simple model of the most likely number of impacts also possesses a sudden jump and provides good agreement with the numerical results for large impact probability. A refinement of this model improves the agreement at lower impact probability values.

scholarly journals Bound states of atomic Josephson vortices

2017 ◽  
Vol 95 (4) ◽  
pp. 336-339 ◽  
Author(s):  
Muhammad Irfan Qadir ◽  
Usama Tahir
Keyword(s):  
Bound States ◽  
Coupling Parameter ◽  
Bound State ◽  
Dark Soliton ◽  
Critical Value ◽  
One Dimensional ◽  
Josephson Vortices ◽  
Existence And Stability ◽  
The Stability ◽  
Bose Einstein

We study the existence and stability of the bound state Josephson vortices solution in two parallel quasi one-dimensional coupled Bose–Einstein condensates. The system can be elucidated by linearly coupled Gross–Pitaevskii equations. The purpose of this study is to investigate the effects of altering the strength of coupling between the two condensates over the stability of the bound-state Josephson vortices. It is found that the stability of bound-state Josephson vortices depends on the value of coupling strength. However, at a critical value of coupling parameter, the Josephson vortices solution transforms into a coupled dark soliton.

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