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Ivan Arraut

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Ivan Arraut is a PhD in Physics graduated from Osaka University. He is characterized for working and adapting mathematical tools for multiple disciplines. He is currently an Assistant Professor at the University of Saint Joseph in Macau. His research areas include, Gravity and Cosmology, High Energy Physics, Condensed matter physics, Econophysics and Quantum Finance.
Supervisors: Hideo Kodama and Yutaka Hosotani

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Papers by Ivan Arraut

Maximal extension of the Schwarzschild spacetime inspired by noncommutative geometry

by Davide Batic and Ivan Arraut

Journal of Mathematical Physics, 2010

We derive a transformation of the noncommutative geometry inspired Schwarzschild solution into ne... more

Brazilian Journal of Physics, 2008

The return of the cosmological constant L to explain the accelerated stage of the universe has br... more The return of the cosmological constant L to explain the accelerated stage of the universe has brought back many puzzles and misteries surrounding this constant. These enigmas touch upon the scales set by L, the cosmological aspect, the astrophysical effects of L and its role in quantum gravity. We will briefly discuss all these aspects putting the emphasis on issues not commonly known

[1305.0475] On the astrophysical scales set by

We calculate explicitly the black-hole temperature for the Schwarzschild de-Sitter solution insid... more We calculate explicitly the black-hole temperature for the Schwarzschild de-Sitter solution inside massive gravity by defining the Killing-vector in the direction of the Stückelberg function. We then consider the conditions which an observer in massive gravity has to obey in order to agree with the standard results of General Relativity.

A noncommutative model for a mini black hole

by Davide Batic and Ivan Arraut

Classical and Quantum Gravity, 2009

We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equatio... more We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equations inspired by the non commutative geometry. In the framework of the non commutative geometry this solution is interpreted as a mini black hole which has the Schwarzschild geometry outside the event horizon, but whose standard central singularity is replaced by a self-gravitating droplet. The energy-momentum tensor of the droplet is of the anisotropic fluid obeying a nonlocal equation of state. The radius of the droplet is finite and the pressure, which gives rise to the hydrostatic equilibrium, is positive definite in the interior.

The solution to the Hardy's paradox

arXiv (Cornell University), Apr 29, 2021

By using both, the weak-value formulation as well as the standard probabilistic approach, we anal... more By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter () which eliminates the assumption of complete annihilation when both, the electron and the positron departing from a common origin, cross the intersection point P. We then find then that the paradox does not exist for all the possible values taken by the parameter. We show that is related to the simultaneity condition at the intersection point P , where the electron and positron meet. In this way, the solution of the paradox is a consequence of the fact that for the case where the electron and the positron interfere with each other, they both cross the intersection point P but not simultaneously, but rather at different times. This is due to the uncertainty associated to the time-coordinate (times of arrival at the point P). Then the Hardy's experiment is an interesting manifestation of the Quantum nature of the spacetime.

On the probability flow in the Stock market I: The Black-Scholes case

arXiv (Cornell University), Dec 19, 2019

It is known that the probability is not a conserved quantity in the stock market, given the fact ... more It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of probability affects the stability of the prices of the Stocks. Finally, we find the conditions under which the probability might be conserved in the market, challenging in this way the non-Hermitian nature of the Black-Scholes Hamiltonian.

$Research paper thumbnail of The Vainshtein conditions: The Vainshtein mechanism in terms of St\"uckelberg functions$

The Vainshtein conditions: The Vainshtein mechanism in terms of St\"uckelberg functions

arXiv (Cornell University), Apr 2, 2015

Here I develop the simplest method in order to evaluate whether or not the Vainshtein mechanism c... more Here I develop the simplest method in order to evaluate whether or not the Vainshtein mechanism can operate for a given set of parameters in a given solution. The method is based on the formulation of the mechanism in terms of the Stückelberg functions given in Int.J.Mod.Phys. D24 (2015) 1550022 and arXiv:1305.0475 [gr-qc]. In such a case, the Vainshtein scale appears as an extremal condition of the dynamical metric. If we fix the graviton mass, we can define the effective Vainshtein scale. Then for parameters where the Vainshtein scale vanishes or becomes smaller than the gravitational radius, the mechanism should be absent. At the other extreme, if the Vainshtein scale is finite or infinite, then the mechanism can operate. For consistency, if we define the Vainshtein scale as an invariant, then we should expect the effective graviton mass to become very large when the Vainshtein mechanism operates. On the other hand, if the mass scale tends to zero, then the extra-degrees of freedom are free to propagate. For clarity, here I analyze the effective mass behavior for the different type of modes.

Research and Technology Development Achievements During the COVID-19 Pandemic—An Overview

Springer eBooks, 2022

Order parameter conditions from mutual information and symmetry conditions

arXiv (Cornell University), Feb 4, 2021

The mutual information method has demonstrated to be very useful for deriving the potential order... more The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the definition. The method then results inefficient for cases where we have order parameters with a large number of constants in the expansion, which happens when we have many degenerate vacuums. Here we introduce some additional constraints based on the existence of broken symmetries, which help us to reduce the arbitrariness in the definitions of the order parameter in the proposed mutual information method.

On the multiplicity of the martingale condition: Spontaneous symmetry breaking in Quantum Finance

arXiv (Cornell University), Apr 18, 2020

We demonstrate that the martingale condition in the stock market can be interpreted as a vacuum c... more We demonstrate that the martingale condition in the stock market can be interpreted as a vacuum condition when we express the financial equations in the Hamiltonian form. We then show that the symmetry under the changes of the prices is spontaneously broken in general and the symmetry under changes in the volatility, for the case of the Merton-Garman (MG) equation, is also spontaneously broken. This reproduces a vacuum degeneracy for the system. In this way, we find the conditions under which, the martingale condition can be considered to be a non-degenerate vacuum. This gives us a surprising connection between spontaneous symmetry breaking and the flow of information through the boundaries for the financial systems. Subsequently, we find an extended martingale condition for the MG equation, depending not only prices but also on the volatility and finally, we show what happens if we include additional non-derivative terms on the Black Scholes and on the MG equations, breaking then some other symmetries of the system spontaneously.

Dark matter and dark energy as a possible manifestation of a fundamental scale

RESCEU Symposium on General Relativity and Gravitation, JGRG 22, 2012

A q -deformation of the Bogoliubov transformations

Physics Letters A, 2018

An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module ... more An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Finally, we introduce a Hopf structure when q is a root of unity.

Black-Hole evaporation and quantum-depletion in Bose–Einstein condensates

arXiv: Quantum Gases, 2020

We study the analogy between the Hawking radiation in Black-Holes and the Quantum depletion proce... more We study the analogy between the Hawking radiation in Black-Holes and the Quantum depletion process of a Bose-Einstein condensate by using the Bogoliubov transformations method. We find that the relation between the Bogoliubov coefficients is similar in both cases (in the appropriate regimes). We then connect the condensate variables with those associated to the Black-Hole, demonstrating then that the zero temperature regime of the condensate is equivalent to the existence of an event horizon in gravity.

The Hawking radiation in massive gravity: Path integral and the Bogoliubov method

arXiv: General Physics, 2017

We proof the consistency of the different approaches for deriving the black-hole radiation for th... more We proof the consistency of the different approaches for deriving the black-hole radiation for the spherically symmetric case inside the theory of massive gravity. By comparing the results obtained by using the Bogoliubov transformations with those obtained by using the path-integral formulation, we find that in both cases the presence of the extra-degrees of freedom create the effect of extra-particles creation due to the distortions on the notions of time defined by the different observers at large scales. This however does not mean extra-particle creation at the horizon level.

Vacuum degeneracy = Multiplicity of Vainshtein scales

arXiv: General Relativity and Quantum Cosmology, 2015

The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions... more The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions of the non-linear formulations of massive gravity. When the gravitational effects are taken into account, and the observers are located at the Vainshtein radius, this degeneracy corresponds to a multiplicity of Vainshtein scales, all of them connected through the broken generators of the theory.

J an 2 01 8 A q-deformation of the Bogoliubov transformations

An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module ... more An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an ∗-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Finally, we introduce a Hopf structure when q is a root of unity.

Dark matter and dark energy as a single manifestation of a fundamental length scale

Testing some scenarios in modified gravity

Spontaneous symmetry breaking as a triangular relation between pairs of Goldstone bosons and the degenerate vacuum: Interactions of D-branes

arXiv: General Physics, 2017

We formulate the Nambu-Goldstone theorem as a triangular relation between pairs of Goldstone boso... more We formulate the Nambu-Goldstone theorem as a triangular relation between pairs of Goldstone bosons with the degenerate vacuum. The vacuum degeneracy is then a natural consequence of this relation. Inside the scenario of String Theory, we then find that there is a correspondence between the way how the $D$-branes interact and the properties of the Goldstone bosons.

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

Mathematics, 2021

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the marting... more The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.

Maximal extension of the Schwarzschild spacetime inspired by noncommutative geometry

by Davide Batic and Ivan Arraut

Journal of Mathematical Physics, 2010

We derive a transformation of the noncommutative geometry inspired Schwarzschild solution into ne... more

Brazilian Journal of Physics, 2008

The return of the cosmological constant L to explain the accelerated stage of the universe has br... more The return of the cosmological constant L to explain the accelerated stage of the universe has brought back many puzzles and misteries surrounding this constant. These enigmas touch upon the scales set by L, the cosmological aspect, the astrophysical effects of L and its role in quantum gravity. We will briefly discuss all these aspects putting the emphasis on issues not commonly known

[1305.0475] On the astrophysical scales set by

We calculate explicitly the black-hole temperature for the Schwarzschild de-Sitter solution insid... more We calculate explicitly the black-hole temperature for the Schwarzschild de-Sitter solution inside massive gravity by defining the Killing-vector in the direction of the Stückelberg function. We then consider the conditions which an observer in massive gravity has to obey in order to agree with the standard results of General Relativity.

A noncommutative model for a mini black hole

by Davide Batic and Ivan Arraut

Classical and Quantum Gravity, 2009

We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equatio... more We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equations inspired by the non commutative geometry. In the framework of the non commutative geometry this solution is interpreted as a mini black hole which has the Schwarzschild geometry outside the event horizon, but whose standard central singularity is replaced by a self-gravitating droplet. The energy-momentum tensor of the droplet is of the anisotropic fluid obeying a nonlocal equation of state. The radius of the droplet is finite and the pressure, which gives rise to the hydrostatic equilibrium, is positive definite in the interior.

The solution to the Hardy's paradox

arXiv (Cornell University), Apr 29, 2021

By using both, the weak-value formulation as well as the standard probabilistic approach, we anal... more By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter () which eliminates the assumption of complete annihilation when both, the electron and the positron departing from a common origin, cross the intersection point P. We then find then that the paradox does not exist for all the possible values taken by the parameter. We show that is related to the simultaneity condition at the intersection point P , where the electron and positron meet. In this way, the solution of the paradox is a consequence of the fact that for the case where the electron and the positron interfere with each other, they both cross the intersection point P but not simultaneously, but rather at different times. This is due to the uncertainty associated to the time-coordinate (times of arrival at the point P). Then the Hardy's experiment is an interesting manifestation of the Quantum nature of the spacetime.

On the probability flow in the Stock market I: The Black-Scholes case

arXiv (Cornell University), Dec 19, 2019

It is known that the probability is not a conserved quantity in the stock market, given the fact ... more It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of probability affects the stability of the prices of the Stocks. Finally, we find the conditions under which the probability might be conserved in the market, challenging in this way the non-Hermitian nature of the Black-Scholes Hamiltonian.

$Research paper thumbnail of The Vainshtein conditions: The Vainshtein mechanism in terms of St\"uckelberg functions$

The Vainshtein conditions: The Vainshtein mechanism in terms of St\"uckelberg functions

arXiv (Cornell University), Apr 2, 2015

Here I develop the simplest method in order to evaluate whether or not the Vainshtein mechanism c... more Here I develop the simplest method in order to evaluate whether or not the Vainshtein mechanism can operate for a given set of parameters in a given solution. The method is based on the formulation of the mechanism in terms of the Stückelberg functions given in Int.J.Mod.Phys. D24 (2015) 1550022 and arXiv:1305.0475 [gr-qc]. In such a case, the Vainshtein scale appears as an extremal condition of the dynamical metric. If we fix the graviton mass, we can define the effective Vainshtein scale. Then for parameters where the Vainshtein scale vanishes or becomes smaller than the gravitational radius, the mechanism should be absent. At the other extreme, if the Vainshtein scale is finite or infinite, then the mechanism can operate. For consistency, if we define the Vainshtein scale as an invariant, then we should expect the effective graviton mass to become very large when the Vainshtein mechanism operates. On the other hand, if the mass scale tends to zero, then the extra-degrees of freedom are free to propagate. For clarity, here I analyze the effective mass behavior for the different type of modes.

Research and Technology Development Achievements During the COVID-19 Pandemic—An Overview

Springer eBooks, 2022

Order parameter conditions from mutual information and symmetry conditions

arXiv (Cornell University), Feb 4, 2021

The mutual information method has demonstrated to be very useful for deriving the potential order... more The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the definition. The method then results inefficient for cases where we have order parameters with a large number of constants in the expansion, which happens when we have many degenerate vacuums. Here we introduce some additional constraints based on the existence of broken symmetries, which help us to reduce the arbitrariness in the definitions of the order parameter in the proposed mutual information method.

On the multiplicity of the martingale condition: Spontaneous symmetry breaking in Quantum Finance

arXiv (Cornell University), Apr 18, 2020

We demonstrate that the martingale condition in the stock market can be interpreted as a vacuum c... more We demonstrate that the martingale condition in the stock market can be interpreted as a vacuum condition when we express the financial equations in the Hamiltonian form. We then show that the symmetry under the changes of the prices is spontaneously broken in general and the symmetry under changes in the volatility, for the case of the Merton-Garman (MG) equation, is also spontaneously broken. This reproduces a vacuum degeneracy for the system. In this way, we find the conditions under which, the martingale condition can be considered to be a non-degenerate vacuum. This gives us a surprising connection between spontaneous symmetry breaking and the flow of information through the boundaries for the financial systems. Subsequently, we find an extended martingale condition for the MG equation, depending not only prices but also on the volatility and finally, we show what happens if we include additional non-derivative terms on the Black Scholes and on the MG equations, breaking then some other symmetries of the system spontaneously.

Dark matter and dark energy as a possible manifestation of a fundamental scale

RESCEU Symposium on General Relativity and Gravitation, JGRG 22, 2012

A q -deformation of the Bogoliubov transformations

Physics Letters A, 2018

An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module ... more An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Finally, we introduce a Hopf structure when q is a root of unity.

Black-Hole evaporation and quantum-depletion in Bose–Einstein condensates

arXiv: Quantum Gases, 2020

We study the analogy between the Hawking radiation in Black-Holes and the Quantum depletion proce... more We study the analogy between the Hawking radiation in Black-Holes and the Quantum depletion process of a Bose-Einstein condensate by using the Bogoliubov transformations method. We find that the relation between the Bogoliubov coefficients is similar in both cases (in the appropriate regimes). We then connect the condensate variables with those associated to the Black-Hole, demonstrating then that the zero temperature regime of the condensate is equivalent to the existence of an event horizon in gravity.

The Hawking radiation in massive gravity: Path integral and the Bogoliubov method

arXiv: General Physics, 2017

We proof the consistency of the different approaches for deriving the black-hole radiation for th... more We proof the consistency of the different approaches for deriving the black-hole radiation for the spherically symmetric case inside the theory of massive gravity. By comparing the results obtained by using the Bogoliubov transformations with those obtained by using the path-integral formulation, we find that in both cases the presence of the extra-degrees of freedom create the effect of extra-particles creation due to the distortions on the notions of time defined by the different observers at large scales. This however does not mean extra-particle creation at the horizon level.

Vacuum degeneracy = Multiplicity of Vainshtein scales

arXiv: General Relativity and Quantum Cosmology, 2015

The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions... more The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions of the non-linear formulations of massive gravity. When the gravitational effects are taken into account, and the observers are located at the Vainshtein radius, this degeneracy corresponds to a multiplicity of Vainshtein scales, all of them connected through the broken generators of the theory.

J an 2 01 8 A q-deformation of the Bogoliubov transformations

An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module ... more An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an ∗-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Finally, we introduce a Hopf structure when q is a root of unity.

Dark matter and dark energy as a single manifestation of a fundamental length scale

Testing some scenarios in modified gravity

Spontaneous symmetry breaking as a triangular relation between pairs of Goldstone bosons and the degenerate vacuum: Interactions of D-branes

arXiv: General Physics, 2017

We formulate the Nambu-Goldstone theorem as a triangular relation between pairs of Goldstone boso... more We formulate the Nambu-Goldstone theorem as a triangular relation between pairs of Goldstone bosons with the degenerate vacuum. The vacuum degeneracy is then a natural consequence of this relation. Inside the scenario of String Theory, we then find that there is a correspondence between the way how the $D$-branes interact and the properties of the Goldstone bosons.

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

Mathematics, 2021

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the marting... more The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.