arXiv subjects

Orion Ciftja

Publications and source records attributed to Orion Ciftja.

13 recordsLinked to original sources

arXiv2025

On the distribution of charges in a conducting needle

We study the distribution of point charges in a straight conductive needle and the electric field created by them. Starting from the bead model with $n$ point charges on the needle, we show the existence and uniqueness of an equilibrium state. We also study the differential system pertaining to the system and show that the system of point charges does not converge towards an equilibrium state. In order to move from a discrete to a continuous model we increase the number of the point charges and explain the paradoxical convergence towards a uniform distribution although the charges tend to accumulate towards the ends of the needle (both at equilibrium and for the differential system of equations describing the Newtonian motion). This convergence has to be understood as that of the distribution functions of a sequence of probabilities (whether it is at equilibrium or when the charges move). We also provide visual illustrations that help understanding the studied phenomena.

math-ph↗

arXiv2025

Modeling the Electrostatic Potential of Disks with Arbitrary Radial Charge Profiles

In this work, we present an analytical study of the electrostatic potential generated by a charged disk with a surface charge distribution that possesses radial axial symmetry. We express the potential in cylindrical coordinates and apply a Bessel function representation for the Coulomb kernel to simplify its calculation. We consider a broad family of surface charge densities and derive an exact expression for the potential based on a classical integral identity involving Bessel functions. This general formulation includes several important special cases such as the uniformly charged disk and edge-concentrated charge density distributions. We explore how variations in various parameters affect the resulting potential, thereby illustrating the influence of radial charge modulation. It is found that the potential undergoes a qualitative change of behavior when the chosen set of parameters is varied. The results are analytically elegant and computationally efficient as all functions involved are implemented in standard scientific computing libraries.

physics.class-ph↗

arXiv2021

Statistical interaction description of Pauli crystals in two-dimensional systems of harmonically confined fermions

It has been conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures, called Pauli crystals, are predicted for a two-dimensional system of free fermions under harmonic confinement. It is assumed that the system consists of neutral fermionic atoms with their spins frozen (spin-polarized) in order to avoid any form of electromagnetic interaction. These crystalline patterns emerge as the most frequent configurations seen in a large collection of single-shot pictures of the system. In this work, we pursue the possibility of this outcome and consider a theoretical model that may capture both qualitatively and quantitatively key features of the above mentioned setup. Our approach treats a quantum system of non-interacting fermions as an effective classical system of particles that interact with an effective statistical interaction potential that mimics the quantum statistics. For this model, we consider two-dimensional few-body systems of harmonically confined particles that interact with a statistical potential and calculate analytically the minimum energy configuration for specific values of relevant parameters. The results for N=3 and 6 particles show that the minimum energy configuration corresponds to and is in good quantitative agreement with the reported values of Pauli crystals seen in single-shot imaging data obtained via the configuration density technique. Numerical results for larger systems of N=15 and 30 particles show that the crystalline configurations observed are not the same as the classical Wigner crystal structures that emerge should the confined charged particles interact with a Coulomb potential. An important question floated is whether such structures do really exist in a quantum system.

quant-ph↗

arXiv2017

Anisotropic magnetoresistance and piezoelectric effect in GaAs Hall samples

In this work, we argue that an anisotropic interaction potential may stabilize anisotropic liquid phases of electrons even in a strong magnetic field regime where normally one expects to see only isotropic quantum Hall or isotropic Fermi liquid states. We use this approach to support a theoretical framework that envisions the possibility of an anisotropic liquid crystalline state of electrons in the lowest Landau level. In particular, we argue that an anisotropic liquid state of electrons may stabilize in the lowest Landau level close to the liquid-solid transition region at filling factor $ν=1/6$ for a given anisotropic Coulomb interaction potential. Quantum Monte Carlo simulations for a liquid crystalline state with broken rotational symmetry indicate stability of liquid crystalline order consistent with the existence of an anisotropic liquid state of electrons stabilized by anisotropy at filling factor $ν=1/6$ of the lowest Landau level.

cond-mat.str-el↗

arXiv2009

Does a Fermi liquid on a half-filled Landau level have Pomeranchuk instabilities?

We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form $ν=2n+1/2$). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the $n \to \infty$ limit.

cond-mat.mes-hall↗

arXiv2007

Monte Carlo simulation method for Laughlin-like states in a disk geometry

We discuss an alternative accurate Monte Carlo method to calculate the ground-state energy and related quantities for Laughlin states of the fractional quantum Hall effect in a disk geometry. This alternative approach allows us to obtain accurate bulk regime (thermodynamic limit) values for various quantities from Monte Carlo simulations with a small number of particles (much smaller than that needed with standard Monte Carlo approaches).

cond-mat.mes-hall↗

arXiv2007

Two-dimensional quantum-dot helium in a magnetic field: Variational theory

A trial wave function for two-dimensional quantum dot helium in an arbitrary perpendicular magnetic field (a system of two interacting electrons in a two-dimensional parabolic confinement potential) is introduced. A key ingredient of this trial wave function is a Jastrow pair correlation factor that has a displaced Gaussian form. The above choice of the pair correlation factor is instrumental on assuring the overall quality of the wave function at all values of the magnetic field.Exact numerical diagonalization results are used to gauge the quality of the proposed trial wave function.We find out that this trial wave function is an excellent representation of the true ground state at all values of the magnetic field including weak (or zero) and strong magnetic fields.

cond-mat.mes-hall↗

arXiv2007

Monte Carlo study of Bose Laughlin wave function for filling factors 1/2, 1/4 and 1/6

Strongly correlated two-dimensional electronic systems subject to a perpendicular magnetic field at lowest Landau level (LLL) filling factors: 1/2, 1/4 and 1/6 are believed to be composite fermion (CF) Fermi liquid phases. Even though a Bose Laughlin wave function cannot describe these filling factors we investigate whether such a wave function provides a lower energy bound to the true CF Fermi liquid energies. By using Monte Carlo simulations in disk geometry we compute the Bose Laughlin energies and compare them to corresponding results for the spin-polarized LLL CF Fermi liquid state and avalable data from literature.We find the unexpected result that, for filling factors 1/4 and 1/6, the Bose Laughlin ground state energy is practically identical to the true CF liquid energy while this is not the case at 1/2 where the Bose Laughlin ground state energy is sizeably lower than the energy of the CF Fermi liquid state.

cond-mat.str-el↗

arXiv2003

Liquid crystalline states for two-dimensional electrons in strong magnetic fields

Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma (2DOCP), we investigate the possibility of liquid crystalline states in a single Landau level (LL). We introduce many-body trial wavefunctions that are translationally invariant but posess 2-fold (i.e. {\em nematic}), 4-fold ({\em tetratic}) or 6-fold ({\em hexatic}) broken rotational symmetry at respective filling factors $ν= 1/3$, 1/5 and 1/7 of the valence LL. We find that the above liquid crystalline states exhibit a soft charge density wave (CDW) which underlies the translationally invariant state but which is destroyed by quantum fluctuations. By means of Monte Carlo (MC) simulations, we determine that, for a considerable variety of interaction potentials, the anisotropic states are energetically unfavorable for the lowest and first excited LL's (with index $L = 0, 1$), whereas the nematic is favorable at the second excited LL ($L = 2$).

cond-mat.mes-hall↗

arXiv2003

Short time evolved wave functions for solving quantum many-body problems

The exact ground state of a strongly interacting quantum many-body system can be obtained by evolving a trial state with finite overlap with the ground state to infinite imaginary time. In this work, we use a newly discovered fourth order positive factorization scheme which requires knowing both the potential and its gradients. We show that the resultaing fourth order wave function alone, without further iterations, gives an excellent description of strongly interacting quantum systems such as liquid 4He, comparable to the best variational results in the literature.

cond-mat↗

arXiv2001

Fermi hypernetted-chain study of half-filled Landau levels with broken rotational symmetry

We investigate broken rotational symmetry (BRS) states at half-filling of the valence Landau level (LL). We generalize Rezayi-Read's (RR) composite fermion (CF) trial wavefunctions to include anisotropic coupling of the flux quanta to electrons, thus generating a nematic order in the underlying CF liquid. Using the Fermi hypernetted-chain (FHNC) method which readily gives results in the thermodynamic limit, we determine in detail the properties of these states. By using the anisotropic pair distribution and static structure functions we determine the correlation energy and find that, as expected, RR's state is stable in the lowest LL, whereas BRS states may occur at half-filling of higher LLs, with possible connection to the recently discovered quantum Hall liquid crystals.

cond-mat.mes-hall↗

arXiv2001

Hypernetted-chain study of broken rotational symmetry states for the $\bmν$ = 1/3 fractional quantum Hall effect and other fractionally filled Landau levels

We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQHE) at 1/3-filling of the valence Landau level (LL). Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens.\ Matter {\bf 8}, L105 (1996)] suggest that Laughlin's state becomes unstable to a BRS state for some critical finite thickness value. We study in detail the properties of such state by performing a hypernetted-chain calculation that gives results in the thermodynamic limit, complementing other methods which are limited to a finite number of particles. Our results indicate that while Laughlin's state is stable in the lowest LL, in higher LLs a BRS instability occurs, perhaps indicating the absence of FQHE at partial fillings of higher LLs. Possible connections to the newly discovered liquid crystalline phases in higher LLs are also discussed.

cond-mat.mes-hall↗

arXiv2000

A ^4He shadow wavefunction with an inverse seventh power particle-particle correlation function

Many ground state studies of $^4$He using a shadow wave function with an inverse fifth power McMillan particle-particle correlation function have yielded radial distribution functions with misplaced peaks. It has been conjectured that this is due to the specific choice of the McMillan correlation function. However, beyond the use of fully optimized two-particle correlation functions, there has been little study of simple alternatives that can correct this defect. In this work we show that the remedy is surprisingly simple. When a shadow wavefunction with an inverse seventh power particle-particle correlation function is used to study $^4$He, it gives a correctly peaked radial distribution function, lowers the energy at all liquid and solid densities, and produces an excellent equation of state.

cond-mat↗