At low temperatures, two-dimensional electron systems in a perpendicular magnetic field exhibit r... more At low temperatures, two-dimensional electron systems in a perpendicular magnetic field exhibit remarkable quantum phenomena [1]. The strongly correlated electrons stabilize in different quantum phases as the quantum Hall filling factor is varied. In this work, we present finite-size Monte Carlo simulation results for anisotropic quantum Hall liquid states observed at certain even-denominator quantum Hall filling factors. The anisotropic phases are described by means of a broken rotational symmetry wave function [2]. Our energy investigations of two-dimensional few electron systems in disk geometry [3] indicate that an anisotropic quantum Hall phase with broken rotational symmetry is energetically favored relative to an isotropic liquid one.
We investigate broken rotational symmetry ͑BRS͒ states at half-filling of the valence Landau leve... more We investigate broken rotational symmetry ͑BRS͒ states at half-filling of the valence Landau level ͑LL͒. We generalize Rezayi and Read's ͑RR͒ trial wave function, a special case of Jain's composite fermion ͑CF͒ wave functions, 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 method, which readily gives results in the thermodynamic limit, we determine the properties of these states in detail. 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 LL's, with a possible connection to the recently discovered quantum Hall liquid crystals.
We present mathematical transformations which allow us to calculate the spin dynamics of an ultra... more We present mathematical transformations which allow us to calculate the spin dynamics of an ultra-small nanoscale molecular magnet consisting of a dimer system of classical (high) Heisenberg spins. We derive exact analytic expressions (in integral form) for the time-dependent spin autocorrelation function and several other quantities. The properties of the time-dependent spin autocorrelation function in terms of various coupling parameters and temperature are discussed in detail.
Many ground state studies of 4 He using a shadow wave function with an inverse fifth power McMill... more 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.
... M 0). It means that a coupled inversion or a spin pairing across the chains is present, ie, w... more ... M 0). It means that a coupled inversion or a spin pairing across the chains is present, ie, when a spin in one site of the rung is flipping up its partner in the other site of the same rung is turning down or vice versa. ... Page 6. 158 R. MEJDANI, A. GASHI, 0. CIFTJA, and A. LAMBROS ...
We propose a new variational wavefunction to describe spin-dependent systems. Spin coherent state... more We propose a new variational wavefunction to describe spin-dependent systems. Spin coherent states are used to represent the spin state of particles. Since states are parameterized by a continuous variable, correlation operators can be represented as simple integrals over c-valued functions. These integrals are simulated using standard Monte Carlo techniques. We present a general N-particle wavefunction written in the coherent state basis. Explicit Monte Carlo calculations on liquid aHe using this wavefunction give very good agreement with standard methods.
Normally, CoFe 2 O 4 has been known as ferromagnetic ferrite with a quite large magnetic moment. ... more Normally, CoFe 2 O 4 has been known as ferromagnetic ferrite with a quite large magnetic moment. However, since we aim to inject the particles into the human body, we are also interested in ZnFe 2 O 4 because in the human body, Fe and Zn exist, so that adding ZnFe 2 O 4 is safer. In both cases, the nanoparticles are coated by silica in order to get rid of toxicity. Our main purpose is to test whether these nanoparticles affect the contractile function of heart cells. Our results on rat's heart cells have shown that both Zn and Co ferrites improved the contractility of heart cells. Notably, although both nanoparticles increased contraction and delayed relaxation, Co ferrites induced a greater contraction but with a slower relaxation. We can theoretically argue that the magnetization effects of the quantum dots have a considerable effect on the pulsating properties of the heart cells. Through this effect, the locally applied magnetic field is able to induce as well as turn on/off various regular beating patterns, thus, resetting the heart beatings.
We consider a quantum Hall system of electrons confined to the uppermost Landau level and assume ... more We consider a quantum Hall system of electrons confined to the uppermost Landau level and assume that the lower Landau levels are full and inert causing no Landau level mixing. While it is known that the problem of electrons interacting with the Coulomb interaction in a higher Landau level is mathematically equivalent to the problem of electrons in the lowest Landau level interacting with an effective interaction, the way the effective interaction can be calculated is not unique. We focus on the details of two different calculations of such effective interaction potentials in the uppermost Landau level and discuss the influence of one or another form of the effective potential on the stability of various correlated electronic phases in the quantum Hall regime.
The hypernetted-chain theory is applied to study hierarchical states in the fractional quantum Ha... more The hypernetted-chain theory is applied to study hierarchical states in the fractional quantum Hall effect. It is noted that a class of wave functions introduced by Girvin ͓Phys. Rev. B 29, 6012 ͑1984͔͒ and MacDonald, Aers, and Dharma-wardana ͓Phys. Rev. B 31, 5529 ͑1985͔͒, based on charge-conjugation procedures, is of the extended shadow wave-function type. The correlation energy, pair distribution function, and static structure function have been calculated in the thermodynamic limit at various filling factors. The results obtained agree with those of previous calculations performed with a finite number of electrons. ͓S0163-1829͑97͒08516-0͔
We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (fill... more 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 → ∞ limit.
The Fermi hypernetted-chain theory is applied to study the half-filled state of the fractional qu... more The Fermi hypernetted-chain theory is applied to study the half-filled state of the fractional quantum Hall effect in the thermodynamic limit. We study in detail the radial distribution function, the correlation energy, and the quasiparticle-quasihole excitation spectrum of an unprojected Fermi wave function of the form ϭ1/2 Fermi ϭ⌸ jϽk N (z j Ϫz k) 2 Det͕ k ជ (r ជ)͖, a possible candidate to describe the half-filled state. Adopting a technique originating from nuclear physics, we compute the effective mass of the fermion excitations near the Fermi surface for this wave function. We find it to be exactly the bare mass of the electron, in accordance with the mean field approximation of not imposing the lowest Landau level constraint. Similar calculations were performed on other related wave functions, which, based on the composite fermion picture, describe the half-filled state of the electrons as a limit of infinite-filled composite fermion Landau levels. ͓S0163-1829͑98͒01736-6͔
The microscopic approach for studying the half-filled state of the fractional quantum Hall effect... more The microscopic approach for studying the half-filled state of the fractional quantum Hall effect is based on the idea of proposing a trial Fermi wave function of the Jastrow-Slater form, which is then fully projected onto the lowest Landau level. A simplified starting point is to drop the projection operator and to consider an unprojected wave function. A recent study claims that such a wave function approximated in a Jastrow form may still constitute a good starting point on the study of the half-filled state. In this paper we formalize the effective hypernetted-chain approximation and apply it to the unprojected Fermi wave function, which describes the even-denominator-filling states. We test the above approximation by using the Fermi hypernettedchain theory, which constitutes the natural choice for the present case. Our results suggest that the approximation of the Slater determinant of plane waves as a Jastrow wave function may not be a very accurate approximation. We conclude that the lowest Landau-level projection operator cannot be neglected if one wants a better quantitative understanding of the phenomena. ͓S0163-1829͑99͒01416-2͔
We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQ... more 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 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.
We consider a ferrofluid system consisting of magnetic particles interacting with a magnetic dipo... more We consider a ferrofluid system consisting of magnetic particles interacting with a magnetic dipoledipole interaction. We study the strong magnetic field regime where all magnetic dipoles are completely polarized in the direction of the magnetic field. We introduce a lattice gas model that serves to describe space ordering phenomena in such systems. It is found that, within mean field theory, this model predicts a second order phase transition to a phase with inhomogeneous lamellar-like ordering below a certain critical temperature.
Physica E: Low-dimensional Systems and Nanostructures, 2001
The most prominent ÿlling factors of the fractional quantum Hall e ect are very well described by... more The most prominent ÿlling factors of the fractional quantum Hall e ect are very well described by the Jain's microscopic composite fermion wave function. Through these wave functions, the composite fermion theory recovers the Laughlin's wave function as a special case and exposes itself to rigorous tests. Considering the system as being in the thermodynamic limit and using simple arguments, we give theoretical estimates for the correlation energy corresponding to all unprojected composite fermion wave functions in terms of the accurately known correlation energies of the Laughlin's wave function. The provided theoretical estimates are in very good agreement with available Monte Carlo data extrapolated to the thermodynamic limit. These results can be quite instructive to test the reliability and accuracy of di erent computational methods employed on the study of these phenomena.
At low temperatures, two-dimensional electron systems in a perpendicular magnetic field exhibit r... more At low temperatures, two-dimensional electron systems in a perpendicular magnetic field exhibit remarkable quantum phenomena [1]. The strongly correlated electrons stabilize in different quantum phases as the quantum Hall filling factor is varied. In this work, we present finite-size Monte Carlo simulation results for anisotropic quantum Hall liquid states observed at certain even-denominator quantum Hall filling factors. The anisotropic phases are described by means of a broken rotational symmetry wave function [2]. Our energy investigations of two-dimensional few electron systems in disk geometry [3] indicate that an anisotropic quantum Hall phase with broken rotational symmetry is energetically favored relative to an isotropic liquid one.
We investigate broken rotational symmetry ͑BRS͒ states at half-filling of the valence Landau leve... more We investigate broken rotational symmetry ͑BRS͒ states at half-filling of the valence Landau level ͑LL͒. We generalize Rezayi and Read's ͑RR͒ trial wave function, a special case of Jain's composite fermion ͑CF͒ wave functions, 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 method, which readily gives results in the thermodynamic limit, we determine the properties of these states in detail. 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 LL's, with a possible connection to the recently discovered quantum Hall liquid crystals.
We present mathematical transformations which allow us to calculate the spin dynamics of an ultra... more We present mathematical transformations which allow us to calculate the spin dynamics of an ultra-small nanoscale molecular magnet consisting of a dimer system of classical (high) Heisenberg spins. We derive exact analytic expressions (in integral form) for the time-dependent spin autocorrelation function and several other quantities. The properties of the time-dependent spin autocorrelation function in terms of various coupling parameters and temperature are discussed in detail.
Many ground state studies of 4 He using a shadow wave function with an inverse fifth power McMill... more 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.
... M 0). It means that a coupled inversion or a spin pairing across the chains is present, ie, w... more ... M 0). It means that a coupled inversion or a spin pairing across the chains is present, ie, when a spin in one site of the rung is flipping up its partner in the other site of the same rung is turning down or vice versa. ... Page 6. 158 R. MEJDANI, A. GASHI, 0. CIFTJA, and A. LAMBROS ...
We propose a new variational wavefunction to describe spin-dependent systems. Spin coherent state... more We propose a new variational wavefunction to describe spin-dependent systems. Spin coherent states are used to represent the spin state of particles. Since states are parameterized by a continuous variable, correlation operators can be represented as simple integrals over c-valued functions. These integrals are simulated using standard Monte Carlo techniques. We present a general N-particle wavefunction written in the coherent state basis. Explicit Monte Carlo calculations on liquid aHe using this wavefunction give very good agreement with standard methods.
Normally, CoFe 2 O 4 has been known as ferromagnetic ferrite with a quite large magnetic moment. ... more Normally, CoFe 2 O 4 has been known as ferromagnetic ferrite with a quite large magnetic moment. However, since we aim to inject the particles into the human body, we are also interested in ZnFe 2 O 4 because in the human body, Fe and Zn exist, so that adding ZnFe 2 O 4 is safer. In both cases, the nanoparticles are coated by silica in order to get rid of toxicity. Our main purpose is to test whether these nanoparticles affect the contractile function of heart cells. Our results on rat's heart cells have shown that both Zn and Co ferrites improved the contractility of heart cells. Notably, although both nanoparticles increased contraction and delayed relaxation, Co ferrites induced a greater contraction but with a slower relaxation. We can theoretically argue that the magnetization effects of the quantum dots have a considerable effect on the pulsating properties of the heart cells. Through this effect, the locally applied magnetic field is able to induce as well as turn on/off various regular beating patterns, thus, resetting the heart beatings.
We consider a quantum Hall system of electrons confined to the uppermost Landau level and assume ... more We consider a quantum Hall system of electrons confined to the uppermost Landau level and assume that the lower Landau levels are full and inert causing no Landau level mixing. While it is known that the problem of electrons interacting with the Coulomb interaction in a higher Landau level is mathematically equivalent to the problem of electrons in the lowest Landau level interacting with an effective interaction, the way the effective interaction can be calculated is not unique. We focus on the details of two different calculations of such effective interaction potentials in the uppermost Landau level and discuss the influence of one or another form of the effective potential on the stability of various correlated electronic phases in the quantum Hall regime.
The hypernetted-chain theory is applied to study hierarchical states in the fractional quantum Ha... more The hypernetted-chain theory is applied to study hierarchical states in the fractional quantum Hall effect. It is noted that a class of wave functions introduced by Girvin ͓Phys. Rev. B 29, 6012 ͑1984͔͒ and MacDonald, Aers, and Dharma-wardana ͓Phys. Rev. B 31, 5529 ͑1985͔͒, based on charge-conjugation procedures, is of the extended shadow wave-function type. The correlation energy, pair distribution function, and static structure function have been calculated in the thermodynamic limit at various filling factors. The results obtained agree with those of previous calculations performed with a finite number of electrons. ͓S0163-1829͑97͒08516-0͔
We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (fill... more 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 → ∞ limit.
The Fermi hypernetted-chain theory is applied to study the half-filled state of the fractional qu... more The Fermi hypernetted-chain theory is applied to study the half-filled state of the fractional quantum Hall effect in the thermodynamic limit. We study in detail the radial distribution function, the correlation energy, and the quasiparticle-quasihole excitation spectrum of an unprojected Fermi wave function of the form ϭ1/2 Fermi ϭ⌸ jϽk N (z j Ϫz k) 2 Det͕ k ជ (r ជ)͖, a possible candidate to describe the half-filled state. Adopting a technique originating from nuclear physics, we compute the effective mass of the fermion excitations near the Fermi surface for this wave function. We find it to be exactly the bare mass of the electron, in accordance with the mean field approximation of not imposing the lowest Landau level constraint. Similar calculations were performed on other related wave functions, which, based on the composite fermion picture, describe the half-filled state of the electrons as a limit of infinite-filled composite fermion Landau levels. ͓S0163-1829͑98͒01736-6͔
The microscopic approach for studying the half-filled state of the fractional quantum Hall effect... more The microscopic approach for studying the half-filled state of the fractional quantum Hall effect is based on the idea of proposing a trial Fermi wave function of the Jastrow-Slater form, which is then fully projected onto the lowest Landau level. A simplified starting point is to drop the projection operator and to consider an unprojected wave function. A recent study claims that such a wave function approximated in a Jastrow form may still constitute a good starting point on the study of the half-filled state. In this paper we formalize the effective hypernetted-chain approximation and apply it to the unprojected Fermi wave function, which describes the even-denominator-filling states. We test the above approximation by using the Fermi hypernettedchain theory, which constitutes the natural choice for the present case. Our results suggest that the approximation of the Slater determinant of plane waves as a Jastrow wave function may not be a very accurate approximation. We conclude that the lowest Landau-level projection operator cannot be neglected if one wants a better quantitative understanding of the phenomena. ͓S0163-1829͑99͒01416-2͔
We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQ... more 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 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.
We consider a ferrofluid system consisting of magnetic particles interacting with a magnetic dipo... more We consider a ferrofluid system consisting of magnetic particles interacting with a magnetic dipoledipole interaction. We study the strong magnetic field regime where all magnetic dipoles are completely polarized in the direction of the magnetic field. We introduce a lattice gas model that serves to describe space ordering phenomena in such systems. It is found that, within mean field theory, this model predicts a second order phase transition to a phase with inhomogeneous lamellar-like ordering below a certain critical temperature.
Physica E: Low-dimensional Systems and Nanostructures, 2001
The most prominent ÿlling factors of the fractional quantum Hall e ect are very well described by... more The most prominent ÿlling factors of the fractional quantum Hall e ect are very well described by the Jain's microscopic composite fermion wave function. Through these wave functions, the composite fermion theory recovers the Laughlin's wave function as a special case and exposes itself to rigorous tests. Considering the system as being in the thermodynamic limit and using simple arguments, we give theoretical estimates for the correlation energy corresponding to all unprojected composite fermion wave functions in terms of the accurately known correlation energies of the Laughlin's wave function. The provided theoretical estimates are in very good agreement with available Monte Carlo data extrapolated to the thermodynamic limit. These results can be quite instructive to test the reliability and accuracy of di erent computational methods employed on the study of these phenomena.
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Papers by O. Ciftja