Arnold Sikkema | Trinity Western University (original) (raw)

Papers by Arnold Sikkema

Physical Review Letters, 1997

We show that the Kondo chain away from half-filling has a spin gap upon the introduction of an ad... more We show that the Kondo chain away from half-filling has a spin gap upon the introduction of an additional direct Heisenberg coupling between localized spins. This is understood in the weak-Kondo-coupling limit of the Heisenberg-Kondo lattice model by bosonization and in the strongcoupling limit by a mapping to a modified t-J model. Only for certain ranges of filling and Heisenberg coupling does the spin gap phase extend from weak to strong coupling.

Physical Review B, 1995

The phase diagram of a one-dimensional tight-binding model with a pair-hopping term (amplitude V)... more The phase diagram of a one-dimensional tight-binding model with a pair-hopping term (amplitude V) has been the subject of some controvery. Using two-loop renormalization group equations and the density matrix renormalization group with lengths L ≤ 60, we argue that no spin-gap transition occurs at half-filling for positive V , contrary to recent claims. However, we point out that away from half-filling, a phase-separation transition occurs at finite V. This transition and the spin-gap transition occuring at half-filling and negative V are analyzed numerically.

Reviewed Title: Morris, Tim, and Don Petcher. Science & Grace: God’s Reign in the Natural Science... more Reviewed Title: Morris, Tim, and Don Petcher. Science & Grace: God’s Reign in the Natural Sciences. Wheaton Illinois: Crossway Books, 2006. 352pp. ISBN 978-1-58134-549-0

New Approaches to the Scientific Study of Religion, 2017

From a consideration of emergence in physics, I outline how reformational philosophical concepts ... more From a consideration of emergence in physics, I outline how reformational philosophical concepts such as idionomy, encapsis, and anticipation can help nuance the claims of emergentism, whether within or beyond the discipline of physics. The methodological reductionist project has given physics significant success from Democritus through Newton to Hawking. Other sciences seek to employ, extend, and emulate physics with its theoretical precision and verisimilitudinous mathematical laws. Triumphalistic practitioners in disciplines from biology through psychology to sociology—hoping to position their theories as inexorable consequences of physics, touted for its firm foundation, solid knowledge, and clear vision—are applauded by public spokespersons of thoroughgoing ontological and naturalistic reductionism. Such optimism persists even when the so-called stratified nature of reality is acknowledged, especially if the concept of emergence is brought into view. But in addition to being poorly defined, emergence is used in exactly opposite senses: claims of unproblematic scientific explanation for a multileveled reality and claims of the intractable impossibility of such explanation. Sometimes enlisted in support of the former is the notion that emergence within physics is fully understood. A sober assessment of predictability and critical realism in physics, however, demonstrates that the nature of emergence within physics renders physics incapable of bearing its supposed grand foundational responsibility. Examples in various physics subfields are analyzed, demonstrating common themes and principles. Collective physical phenomena are strikingly characterized by robustness of the ordered macroscopic whole relative to variations in microscopic parts, universality near phase transitions, and symmetry breaking, but most importantly by surprise and incalculability.

Bulletin of the American Physical Society, 2005

It has been observed that it sometimes seems to rain harder a few seconds after a lightning strik... more It has been observed that it sometimes seems to rain harder a few seconds after a lightning strike (so-called ``rain gush lightning'' phenomenon). The conventional way to study this type of phenomena is with radar. To investigate this in a more direct way, an apparatus was designed and ...

et me begin by quoting John Polkinghorne, theoretical physicist and Anglican priest, as he addres... more et me begin by quoting John Polkinghorne, theoretical physicist and Anglican priest, as he addresses the nature of this presentation. "Interdisciplinary work is both essential (for, in the end, knowledge is one) and risky (for we must all venture to speak on topics of which we are not wholly the master)." 2 A key phrase affirmed by Reformational thinking which upholds a high view of creation is that "knowledge is one"; we believe that "in [Christ] all things hold together" (Col 1:17). I had the pleasure of spending five weeks in the summer of 1998 at Calvin College with Polkinghorne and a dozen other physicists, philosophers, and theologians, and much of what I have to say tonight is influenced by that experience. The doctrine of the providence of God is one of the most cherished truths of Christianity. Article 13 of the Belgic Confession (1561) states that God, having created all things, does not forsake them, but rules and governs them. Chapter V of the Westminster Confession (1648) goes on to say that he uses "means" to "govern all creatures, actions, and 1 This paper was made possible in part through support of The Pew Charitable Trusts and the Seminars in Christian Scholarship program at Calvin College.

An essay review of the treatment of physics and the physical aspect in Jacob Klapwijk, "Purp... more An essay review of the treatment of physics and the physical aspect in Jacob Klapwijk, "Purpose in the Living World? Creation and Emergent Evolution" (Cambridge: Cambridge University Press, 2008).

ABSTRACT It is important to develop a Christian perspective or worldview on how the world “works”... more ABSTRACT It is important to develop a Christian perspective or worldview on how the world “works” and about how God relates to the creation. Without such grounding, we join in some of the fallacies plaguing today’s culture, such as philosophical materialism, naturalism, and the dualisms between science and religion and between the natural and the supernatural. In this article, I will discuss what we — both scientists and members of the general public — mean when we speak about natural scientific laws, or laws of nature, as well as what the Bible says about God’s ordinances for creation, particularly in terms of his showing covenant faithfulness toward his creation. Along the way, we will consider examples of natural scientific laws, and the ways they are used. Habits of mind and ways of thinking relating to science generally will be explored by considering what we have historically understood by natural laws, not only in the grand sweep of the history of science but also in the development, training, and work of individual scientists.

Physical Review D, 1991

ABSTRACT Relativistic wave equations are solved exactly in the classical space-time background of... more ABSTRACT Relativistic wave equations are solved exactly in the classical space-time background of a two-dimensional gravitational theory. In the simplest nontrivial geometry without horizons, the solutions are necessarily bound states and the constraints on the energy eigenvalues are determined. Aspects of quantum field theory in the background of the (1+1)-dimensional black hole are also examined.

Physica B: Condensed Matter, 1995

We examine a model Hamiltonian for the heavy-fermion URu2Si 2 based on two crystal-field-split si... more We examine a model Hamiltonian for the heavy-fermion URu2Si 2 based on two crystal-field-split singlets for the uranium spin coupled by on-site exchange to the conduction electrons. It is equivalent to an Ising-Kondo lattice with transverse magnetic field. Within the mean-field approximation, we find a logarithmic response of the conduction electrons to moment formation. Over an appreciable range of parameters, the moments in the antiferromagnetic state are anomalously small as observed, and a reasonable N6el temperature is obtained. The model also gives a qualitatively correct temperature-dependence, but not magnitude, of the specific heat, and we find that the majority of the specific heat jump at the N6el temperature arises from the formation of a spin gap in the conduction electron spectrum.

Physical Review B, 1996

We study the phase diagram of the Ising-Kondo lattice with transverse magnetic field as a possibl... more We study the phase diagram of the Ising-Kondo lattice with transverse magnetic field as a possible model for the weak-moment heavy-fermion compound URu 2 Si 2 , in terms of two low-lying f singlets in which the uranium moment is coupled by on-site exchange to the conduction electron spins. In the mean-field approximation for an extended range of parameters, we show that the conduction electron magnetization responds logarithmically to f-moment formation, that the ordered moment in the antiferromagnetic state is anomalously small, and that the Néel temperature is of the order observed. The model gives a qualitatively correct temperature-dependence, but not magnitude, of the specific heat. The majority of the specific heat jump at the Néel temperature arises from the formation of a spin gap in the conduction electron spectrum. We also discuss the single-impurity version of the model and speculate on ways to increase the specific heat coefficient. In the limits of small bandwidth and of small Ising-Kondo coupling, we find that the model corresponds to anisotropic Heisenberg and Hubbard models respectively.

Aps Northwest Section Meeting Abstracts, 2006

Phase transitions are well defined in physics through concepts such as spontaneous symmetry break... more Phase transitions are well defined in physics through concepts such as spontaneous symmetry breaking, order parameter, entropy, and critical exponents. But emergence --- also exhibiting whole-part relations (such as top-down influence), unpredictability, and insensitivity to ...

In Dooyeweerd’s modal scale, the physical aspect is flanked by the kinematic and biotic. While ph... more In Dooyeweerd’s modal scale, the physical aspect is flanked by the kinematic and biotic. While physics and mathematics have mutually benefited one another for hundreds of years, connections between biology and physics are only now beginning to emerge. Understanding the defining characteristics of these three disciplines helps detail their mutual irreducibility as well as their possibilities for fruitful engagement, especially when considering the developments of modern physics. Furthermore, a critical-realist and model-oriented approach to the laws of physics can encourage humble epistemology and limited ontology, much needed correctives to rampant reductionist and atheist claims. Casting all this within a trinitarian, covenantal, and creation-fall-redemption narrative, in which divine revelation as well as creation are taken seriously, provides a nuanced perspective which, among other benefits, offers hope for resolving conflicts the scientific community experiences with many laypersons.

We discuss the various themes addressed in the preceding talks in the emergence stream, drawing c... more We discuss the various themes addressed in the preceding talks in the emergence stream, drawing connections with and implications from them. We will also bring forward other relevant issues in emergence by engaging with recent works in fields such as biology, physics, biophysics, biosemiotics, information science, and philosophy of science, particularly being informed by reformational philosophical perspectives. After initial presentations by each panelist, and a brief trialogue among us, we will lead a general conversation with presenters and attendees of the emergence stream. [Audio recording and PDF of screen presentation available online; see links.]

The Future of Creation Order, Proceedings of the Christian Philosophy Conference, Amsterdam, 16-19 August 2011, 2014

From a consideration of emergence in physics, I outline how reformational philosophical concepts ... more From a consideration of emergence in physics, I outline how reformational philosophical concepts such as idionomy, enkapsis, and anticipation can help nuance the claims of emergentism, whether within or beyond the discipline of physics. The methodological reductionist project has given physics significant success from Democritus through Newton to Hawking. Other sciences seek to employ, extend, and emulate physics with its theoretical precision and verisimilitudinous mathematical laws. Triumphalistic practitioners in disciplines from biology through psychology to sociology — hoping to position their theories as inexorable consequences of physics, touted for its firm foundation, solid knowledge, and clear vision — are applauded by public spokespersons of thoroughgoing ontological and naturalistic reductionism. Such optimism persists even when the so-called stratified nature of reality is acknowledged, especially if the concept of emergence is brought into view. But in addition to being poorly defined, emergence is used in exactly opposite senses: claims of unproblematic scientific explanation for a multi-levelled reality and claims of the intractable impossibility of such explanation. Sometimes enlisted in support of the former is the notion that emergence within physics is fully understood. A sober assessment of predictability and critical realism in physics, however, demonstrates that the nature of emergence within physics renders physics incapable of bearing its supposed grand foundational responsibility. Examples in various physics subfields are analyzed, demonstrating common themes and principles. Collective physical phenomena are strikingly characterized by robustness of the ordered macroscopic whole relative to variations in microscopic parts, universality near phase transitions, and symmetry breaking, but most importantly surprise and incalculability.

Physical Review Letters, 1997

We show that the Kondo chain away from half-filling has a spin gap upon the introduction of an ad... more We show that the Kondo chain away from half-filling has a spin gap upon the introduction of an additional direct Heisenberg coupling between localized spins. This is understood in the weak-Kondo-coupling limit of the Heisenberg-Kondo lattice model by bosonization and in the strongcoupling limit by a mapping to a modified t-J model. Only for certain ranges of filling and Heisenberg coupling does the spin gap phase extend from weak to strong coupling.

Physical Review B, 1995

The phase diagram of a one-dimensional tight-binding model with a pair-hopping term (amplitude V)... more The phase diagram of a one-dimensional tight-binding model with a pair-hopping term (amplitude V) has been the subject of some controvery. Using two-loop renormalization group equations and the density matrix renormalization group with lengths L ≤ 60, we argue that no spin-gap transition occurs at half-filling for positive V , contrary to recent claims. However, we point out that away from half-filling, a phase-separation transition occurs at finite V. This transition and the spin-gap transition occuring at half-filling and negative V are analyzed numerically.

Reviewed Title: Morris, Tim, and Don Petcher. Science & Grace: God’s Reign in the Natural Science... more Reviewed Title: Morris, Tim, and Don Petcher. Science & Grace: God’s Reign in the Natural Sciences. Wheaton Illinois: Crossway Books, 2006. 352pp. ISBN 978-1-58134-549-0

New Approaches to the Scientific Study of Religion, 2017

From a consideration of emergence in physics, I outline how reformational philosophical concepts ... more From a consideration of emergence in physics, I outline how reformational philosophical concepts such as idionomy, encapsis, and anticipation can help nuance the claims of emergentism, whether within or beyond the discipline of physics. The methodological reductionist project has given physics significant success from Democritus through Newton to Hawking. Other sciences seek to employ, extend, and emulate physics with its theoretical precision and verisimilitudinous mathematical laws. Triumphalistic practitioners in disciplines from biology through psychology to sociology—hoping to position their theories as inexorable consequences of physics, touted for its firm foundation, solid knowledge, and clear vision—are applauded by public spokespersons of thoroughgoing ontological and naturalistic reductionism. Such optimism persists even when the so-called stratified nature of reality is acknowledged, especially if the concept of emergence is brought into view. But in addition to being poorly defined, emergence is used in exactly opposite senses: claims of unproblematic scientific explanation for a multileveled reality and claims of the intractable impossibility of such explanation. Sometimes enlisted in support of the former is the notion that emergence within physics is fully understood. A sober assessment of predictability and critical realism in physics, however, demonstrates that the nature of emergence within physics renders physics incapable of bearing its supposed grand foundational responsibility. Examples in various physics subfields are analyzed, demonstrating common themes and principles. Collective physical phenomena are strikingly characterized by robustness of the ordered macroscopic whole relative to variations in microscopic parts, universality near phase transitions, and symmetry breaking, but most importantly by surprise and incalculability.

Bulletin of the American Physical Society, 2005

It has been observed that it sometimes seems to rain harder a few seconds after a lightning strik... more It has been observed that it sometimes seems to rain harder a few seconds after a lightning strike (so-called ``rain gush lightning'' phenomenon). The conventional way to study this type of phenomena is with radar. To investigate this in a more direct way, an apparatus was designed and ...

et me begin by quoting John Polkinghorne, theoretical physicist and Anglican priest, as he addres... more et me begin by quoting John Polkinghorne, theoretical physicist and Anglican priest, as he addresses the nature of this presentation. "Interdisciplinary work is both essential (for, in the end, knowledge is one) and risky (for we must all venture to speak on topics of which we are not wholly the master)." 2 A key phrase affirmed by Reformational thinking which upholds a high view of creation is that "knowledge is one"; we believe that "in [Christ] all things hold together" (Col 1:17). I had the pleasure of spending five weeks in the summer of 1998 at Calvin College with Polkinghorne and a dozen other physicists, philosophers, and theologians, and much of what I have to say tonight is influenced by that experience. The doctrine of the providence of God is one of the most cherished truths of Christianity. Article 13 of the Belgic Confession (1561) states that God, having created all things, does not forsake them, but rules and governs them. Chapter V of the Westminster Confession (1648) goes on to say that he uses "means" to "govern all creatures, actions, and 1 This paper was made possible in part through support of The Pew Charitable Trusts and the Seminars in Christian Scholarship program at Calvin College.

An essay review of the treatment of physics and the physical aspect in Jacob Klapwijk, "Purp... more An essay review of the treatment of physics and the physical aspect in Jacob Klapwijk, "Purpose in the Living World? Creation and Emergent Evolution" (Cambridge: Cambridge University Press, 2008).

ABSTRACT It is important to develop a Christian perspective or worldview on how the world “works”... more ABSTRACT It is important to develop a Christian perspective or worldview on how the world “works” and about how God relates to the creation. Without such grounding, we join in some of the fallacies plaguing today’s culture, such as philosophical materialism, naturalism, and the dualisms between science and religion and between the natural and the supernatural. In this article, I will discuss what we — both scientists and members of the general public — mean when we speak about natural scientific laws, or laws of nature, as well as what the Bible says about God’s ordinances for creation, particularly in terms of his showing covenant faithfulness toward his creation. Along the way, we will consider examples of natural scientific laws, and the ways they are used. Habits of mind and ways of thinking relating to science generally will be explored by considering what we have historically understood by natural laws, not only in the grand sweep of the history of science but also in the development, training, and work of individual scientists.

Physical Review D, 1991

ABSTRACT Relativistic wave equations are solved exactly in the classical space-time background of... more ABSTRACT Relativistic wave equations are solved exactly in the classical space-time background of a two-dimensional gravitational theory. In the simplest nontrivial geometry without horizons, the solutions are necessarily bound states and the constraints on the energy eigenvalues are determined. Aspects of quantum field theory in the background of the (1+1)-dimensional black hole are also examined.

Physica B: Condensed Matter, 1995

We examine a model Hamiltonian for the heavy-fermion URu2Si 2 based on two crystal-field-split si... more We examine a model Hamiltonian for the heavy-fermion URu2Si 2 based on two crystal-field-split singlets for the uranium spin coupled by on-site exchange to the conduction electrons. It is equivalent to an Ising-Kondo lattice with transverse magnetic field. Within the mean-field approximation, we find a logarithmic response of the conduction electrons to moment formation. Over an appreciable range of parameters, the moments in the antiferromagnetic state are anomalously small as observed, and a reasonable N6el temperature is obtained. The model also gives a qualitatively correct temperature-dependence, but not magnitude, of the specific heat, and we find that the majority of the specific heat jump at the N6el temperature arises from the formation of a spin gap in the conduction electron spectrum.

Physical Review B, 1996

We study the phase diagram of the Ising-Kondo lattice with transverse magnetic field as a possibl... more We study the phase diagram of the Ising-Kondo lattice with transverse magnetic field as a possible model for the weak-moment heavy-fermion compound URu 2 Si 2 , in terms of two low-lying f singlets in which the uranium moment is coupled by on-site exchange to the conduction electron spins. In the mean-field approximation for an extended range of parameters, we show that the conduction electron magnetization responds logarithmically to f-moment formation, that the ordered moment in the antiferromagnetic state is anomalously small, and that the Néel temperature is of the order observed. The model gives a qualitatively correct temperature-dependence, but not magnitude, of the specific heat. The majority of the specific heat jump at the Néel temperature arises from the formation of a spin gap in the conduction electron spectrum. We also discuss the single-impurity version of the model and speculate on ways to increase the specific heat coefficient. In the limits of small bandwidth and of small Ising-Kondo coupling, we find that the model corresponds to anisotropic Heisenberg and Hubbard models respectively.

Aps Northwest Section Meeting Abstracts, 2006

Phase transitions are well defined in physics through concepts such as spontaneous symmetry break... more Phase transitions are well defined in physics through concepts such as spontaneous symmetry breaking, order parameter, entropy, and critical exponents. But emergence --- also exhibiting whole-part relations (such as top-down influence), unpredictability, and insensitivity to ...

In Dooyeweerd’s modal scale, the physical aspect is flanked by the kinematic and biotic. While ph... more In Dooyeweerd’s modal scale, the physical aspect is flanked by the kinematic and biotic. While physics and mathematics have mutually benefited one another for hundreds of years, connections between biology and physics are only now beginning to emerge. Understanding the defining characteristics of these three disciplines helps detail their mutual irreducibility as well as their possibilities for fruitful engagement, especially when considering the developments of modern physics. Furthermore, a critical-realist and model-oriented approach to the laws of physics can encourage humble epistemology and limited ontology, much needed correctives to rampant reductionist and atheist claims. Casting all this within a trinitarian, covenantal, and creation-fall-redemption narrative, in which divine revelation as well as creation are taken seriously, provides a nuanced perspective which, among other benefits, offers hope for resolving conflicts the scientific community experiences with many laypersons.

We discuss the various themes addressed in the preceding talks in the emergence stream, drawing c... more We discuss the various themes addressed in the preceding talks in the emergence stream, drawing connections with and implications from them. We will also bring forward other relevant issues in emergence by engaging with recent works in fields such as biology, physics, biophysics, biosemiotics, information science, and philosophy of science, particularly being informed by reformational philosophical perspectives. After initial presentations by each panelist, and a brief trialogue among us, we will lead a general conversation with presenters and attendees of the emergence stream. [Audio recording and PDF of screen presentation available online; see links.]

The Future of Creation Order, Proceedings of the Christian Philosophy Conference, Amsterdam, 16-19 August 2011, 2014

From a consideration of emergence in physics, I outline how reformational philosophical concepts ... more From a consideration of emergence in physics, I outline how reformational philosophical concepts such as idionomy, enkapsis, and anticipation can help nuance the claims of emergentism, whether within or beyond the discipline of physics. The methodological reductionist project has given physics significant success from Democritus through Newton to Hawking. Other sciences seek to employ, extend, and emulate physics with its theoretical precision and verisimilitudinous mathematical laws. Triumphalistic practitioners in disciplines from biology through psychology to sociology — hoping to position their theories as inexorable consequences of physics, touted for its firm foundation, solid knowledge, and clear vision — are applauded by public spokespersons of thoroughgoing ontological and naturalistic reductionism. Such optimism persists even when the so-called stratified nature of reality is acknowledged, especially if the concept of emergence is brought into view. But in addition to being poorly defined, emergence is used in exactly opposite senses: claims of unproblematic scientific explanation for a multi-levelled reality and claims of the intractable impossibility of such explanation. Sometimes enlisted in support of the former is the notion that emergence within physics is fully understood. A sober assessment of predictability and critical realism in physics, however, demonstrates that the nature of emergence within physics renders physics incapable of bearing its supposed grand foundational responsibility. Examples in various physics subfields are analyzed, demonstrating common themes and principles. Collective physical phenomena are strikingly characterized by robustness of the ordered macroscopic whole relative to variations in microscopic parts, universality near phase transitions, and symmetry breaking, but most importantly surprise and incalculability.